E. Schuyler, J. A. V. Gross, R. L. Moore, and G. B. M. Zerr :
“Solutions of problems: Algebra: 123 ,”
Amer. Math. Monthly
8 : 10
(October 1901 ),
pp. 196 .
MR
1515377
article
BibTeX
@article {key1515377m,
AUTHOR = {Schuyler, Elmer and Gross, John A. Van
and Moore, R. L. and Zerr, G. B. M.},
TITLE = {Solutions of problems: {A}lgebra: 123},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {The American Mathematical Monthly},
VOLUME = {8},
NUMBER = {10},
MONTH = {October},
YEAR = {1901},
PAGES = {196},
URL = {http://www.jstor.org/stable/2971322},
NOTE = {MR:1515377.},
ISSN = {0002-9890},
}
R. L. Moore and I. M. DeLong :
“Problems for solution: Miscellaneous: 143–144 ,”
Amer. Math. Monthly
11 : 2
(1904 ),
pp. 45 .
MR
1516082
article
BibTeX
@article {key1516082m,
AUTHOR = {Moore, R. L. and DeLong, Ira M.},
TITLE = {Problems for solution: {M}iscellaneous:
143--144},
JOURNAL = {Amer. Math. Monthly},
FJOURNAL = {The American Mathematical Monthly},
VOLUME = {11},
NUMBER = {2},
YEAR = {1904},
PAGES = {45},
URL = {http://www.jstor.org/stable/2967888},
NOTE = {MR:1516082.},
ISSN = {0002-9890},
}
R. L. Moore :
Sets of metrical hypotheses for geometry .
Ph.D. thesis ,
University of Chicago ,
1905 .
Advised by O. Veblen and E. H. Moore .
See also article with the same title in Trans. Am. Math. Soc. 9 :4 (1908) .
MR
2936795
phdthesis
People
BibTeX
@phdthesis {key2936795m,
AUTHOR = {Moore, Robert Lee},
TITLE = {Sets of metrical hypotheses for geometry},
SCHOOL = {University of Chicago},
YEAR = {1905},
URL = {http://search.proquest.com/docview/301704624},
NOTE = {Advised by O. Veblen and E. H. Moore.
See also article with the same title
in \textit{Trans. Am. Math. Soc.} \textbf{9}:4
(1908). MR:2936795.},
}
R. L. Moore :
“Geometry in which the sum of the angles of every triangle is two right angles ,”
Trans. Am. Math. Soc.
8 : 3
(July 1907 ),
pp. 369–378 .
MR
1500791
JFM
38.0503.02
article
BibTeX
@article {key1500791m,
AUTHOR = {Moore, R. L.},
TITLE = {Geometry in which the sum of the angles
of every triangle is two right angles},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {8},
NUMBER = {3},
MONTH = {July},
YEAR = {1907},
PAGES = {369--378},
DOI = {10.2307/1988780},
NOTE = {MR:1500791. JFM:38.0503.02.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“Sets of metrical hypotheses for geometry ,”
Trans. Am. Math. Soc.
9 : 4
(October 1908 ),
pp. 487–512 .
See also Moore’s PhD thesis (1905) .
MR
1500823
JFM
39.0538.06
article
Abstract
BibTeX
In this paper is given a set of assumptions, \( C \) , concerning point, order and congruence, which, together with a certain set of order assumptions \( O \) , a continuity assumption \( K \) , and a very weak parallel assumption \( P_0 \) , are sufficient for the establishment of ordinary Euclidean geometry.
@article {key1500823m,
AUTHOR = {Moore, Robert L.},
TITLE = {Sets of metrical hypotheses for geometry},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {9},
NUMBER = {4},
MONTH = {October},
YEAR = {1908},
PAGES = {487--512},
DOI = {10.2307/1988666},
NOTE = {See also Moore's PhD thesis (1905).
MR:1500823. JFM:39.0538.06.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“On Duhamel’s theorem ,”
Ann. Math. (2)
13 : 1–4
(1911–1912 ),
pp. 161–166 .
MR
1502430
JFM
43.0354.02
article
BibTeX
@article {key1502430m,
AUTHOR = {Moore, R. L.},
TITLE = {On {D}uhamel's theorem},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {13},
NUMBER = {1--4},
YEAR = {1911--1912},
PAGES = {161--166},
DOI = {10.2307/1968084},
NOTE = {MR:1502430. JFM:43.0354.02.},
ISSN = {0003-486X},
CODEN = {ANMAAH},
}
R. L. Moore :
“A note concerning Veblen’s axioms for geometry ,”
Trans. Am. Math. Soc.
13 : 1
(January 1912 ),
pp. 74–76 .
MR
1500906
JFM
43.0560.03
article
BibTeX
@article {key1500906m,
AUTHOR = {Moore, Robert L.},
TITLE = {A note concerning {V}eblen's axioms
for geometry},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {13},
NUMBER = {1},
MONTH = {January},
YEAR = {1912},
PAGES = {74--76},
DOI = {10.2307/1988615},
NOTE = {MR:1500906. JFM:43.0560.03.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“The linear continuum in terms of point and limit ,”
Ann. Math. (2)
16 : 1–4
(1914–1915 ),
pp. 123–133 .
MR
1502498
JFM
45.1219.17
article
Abstract
BibTeX
@article {key1502498m,
AUTHOR = {Moore, Robert L.},
TITLE = {The linear continuum in terms of point
and limit},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {16},
NUMBER = {1--4},
YEAR = {1914--1915},
PAGES = {123--133},
DOI = {10.2307/1968052},
NOTE = {MR:1502498. JFM:45.1219.17.},
ISSN = {0003-486X},
CODEN = {ANMAAH},
}
R. L. Moore :
“On the linear continuum ,”
Bull. Am. Math. Soc.
22 : 3
(1915 ),
pp. 117–122 .
MR
1559727
JFM
45.1345.02
article
Abstract
BibTeX
In [Moore 1915], I proposed a set \( G \) of eight axioms for the linear continuum in terms of point and limit . Betweenness was defined, and it was stated that the set \( G \) is categorical with respect to point and the thus defined betweenness . In the present paper it is shown that, although this statement is true, nevertheless \( G \) is not absolutely categorical, that is to say it is not categorical with respect to point and limit , the undefined symbols in terms of which it is stated.
@article {key1559727m,
AUTHOR = {Moore, R. L.},
TITLE = {On the linear continuum},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {22},
NUMBER = {3},
YEAR = {1915},
PAGES = {117--122},
DOI = {10.1090/S0002-9904-1915-02734-5},
NOTE = {MR:1559727. JFM:45.1345.02.},
ISSN = {0002-9904},
}
R. L. Moore :
“On a set of postulates which suffice to define a number-plane ,”
Trans. Am. Math. Soc.
16 : 1
(January 1915 ),
pp. 27–32 .
MR
1500996
JFM
45.0728.05
article
Abstract
BibTeX
In this paper I propose to show that any plane satisfying Veblen’s Axioms I–VIII, XI of his System of axioms for geometry [1904] is a number-plane, or in other words that any plane \( V \) satisfying these axioms contains a system of continuous curves such that, with reference to these curves regarded as straight lines, the plane \( V \) is an ordinary euclidean plane.
@article {key1500996m,
AUTHOR = {Moore, Robert L.},
TITLE = {On a set of postulates which suffice
to define a number-plane},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {16},
NUMBER = {1},
MONTH = {January},
YEAR = {1915},
PAGES = {27--32},
DOI = {10.2307/1988742},
NOTE = {MR:1500996. JFM:45.0728.05.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“On the foundations of plane analysis situs ,”
Trans. Am. Math. Soc.
17 : 2
(1916 ),
pp. 131–164 .
A brief article with the same title published in Proc. Nat. Acad. Sci. U.S.A. 2 :5 (1916) .
MR
1501033
JFM
46.0828.02
article
Abstract
BibTeX
The present paper contains three systems of axioms, \( \Sigma_1 \) , \( \Sigma_2 \) , and \( \Sigma_3 \) . Each of these systems is a sufficient basis for a considerable body of theorems in the domain of plane analysis situs or what may be roughly termed the nonmetrical part of plane point-set theory, including the theory of plane curves. The axioms of each system are stated in terms of a class of elements called points and a class of point-sets called regions .
@article {key1501033m,
AUTHOR = {Moore, Robert L.},
TITLE = {On the foundations of plane analysis
situs},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {17},
NUMBER = {2},
YEAR = {1916},
PAGES = {131--164},
DOI = {10.2307/1989029},
NOTE = {A brief article with the same title
published in \textit{Proc. Nat. Acad.
Sci. U.S.A.} \textbf{2}:5 (1916). MR:1501033.
JFM:46.0828.02.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“Concerning a non-metrical pseudo-Archimedean axiom ,”
Bull. Am. Math. Soc.
22 : 5
(1916 ),
pp. 225–236 .
MR
1559766
JFM
45.0728.01
article
BibTeX
@article {key1559766m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning a non-metrical pseudo-{A}rchimedean
axiom},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {22},
NUMBER = {5},
YEAR = {1916},
PAGES = {225--236},
DOI = {10.1090/S0002-9904-1916-02764-9},
NOTE = {MR:1559766. JFM:45.0728.01.},
ISSN = {0002-9904},
}
R. L. Moore :
“On the foundations of plane analysis situs ,”
Proc. Nat. Acad. Sci. U.S.A.
2 : 5
(May 1916 ),
pp. 270–272 .
A longer article with the same title was published in Trans. Am. Math. Soc. 17 :2 (1916) .
JFM
46.1498.03
article
BibTeX
@article {key46.1498.03j,
AUTHOR = {Moore, Robert L.},
TITLE = {On the foundations of plane analysis
situs},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {2},
NUMBER = {5},
MONTH = {May},
YEAR = {1916},
PAGES = {270--272},
DOI = {10.1073/pnas.2.5.270},
NOTE = {A longer article with the same title
was published in \textit{Trans. Am.
Math. Soc.} \textbf{17}:2 (1916). JFM:46.1498.03.},
ISSN = {0027-8424},
}
R. L. Moore :
“A theorem concerning continuous curves ,”
Bull. Am. Math. Soc.
23 : 5
(1917 ),
pp. 233–236 .
A related research report was published in Bull. Am. Math. Soc. 23 :4 (1917) .
MR
1559925
JFM
46.0829.05, 46.0308.03
article
Abstract
BibTeX
@article {key1559925m,
AUTHOR = {Moore, R. L.},
TITLE = {A theorem concerning continuous curves},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {23},
NUMBER = {5},
YEAR = {1917},
PAGES = {233--236},
DOI = {10.1090/S0002-9904-1917-02926-6},
NOTE = {A related research report was published
in \textit{Bull. Am. Math. Soc.} \textbf{23}:4
(1917). MR:1559925. JFM:46.0829.05,
46.0308.03.},
ISSN = {0002-9904},
}
R. L. Moore :
“A theorem concerning continuous curves ,”
Bull. Am. Math. Soc.
23 : 4
(1917 ),
pp. 162 .
Research report only.
Article in Bull. Am. Math. Soc. 23 :5 (1917) .
JFM
46.0308.02
article
BibTeX
@article {key46.0308.02j,
AUTHOR = {Moore, R. L.},
TITLE = {A theorem concerning continuous curves},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {23},
NUMBER = {4},
YEAR = {1917},
PAGES = {162},
URL = {http://www.ams.org/journals/bull/1917-23-04/S0002-9904-1917-02891-1/S0002-9904-1917-02891-1.pdf},
NOTE = {Research report only. Article in \textit{Bull.
Am. Math. Soc.} \textbf{23}:5 (1917).
JFM:46.0308.02.},
ISSN = {0002-9904},
}
R. L. Moore :
“A characterization of Jordan regions by properties having no reference to their boundaries ,”
Proc. Nat. Acad. Sci. U.S.A.
4 : 12
(December 1918 ),
pp. 364–370 .
JFM
46.1451.02
article
Abstract
BibTeX
Schoenflies [1902] has formulated a set of conditions under which the common boundary of two domains will be a simple closed curve. A different set has been given by J. R. Kline [1918]. Carathéodory [1912-13] has obtained conditions under which the boundary of a single domain will be such a curve. In each of these treatments, however, conditions are imposed
on the boundary itself,
regarding the relation of the boundary to the domain or domains in question.
In the present paper I propose to establish the following theorem in which all the conditions imposed are on the domain \( R \) alone .
In order that a simply connected, limited, two-dimensional domain \( R \) should have a simple closed curve as its boundary it is necessary and sufficient that \( R \) should be uniformly connected im kleinen.
@article {key46.1451.02j,
AUTHOR = {Moore, R. L.},
TITLE = {A characterization of {J}ordan regions
by properties having no reference to
their boundaries},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {4},
NUMBER = {12},
MONTH = {December},
YEAR = {1918},
PAGES = {364--370},
DOI = {10.1073/pnas.4.12.364},
NOTE = {JFM:46.1451.02.},
ISSN = {0027-8424},
}
R. L. Moore :
“On the Lie–Riemann-Helmholtz–Hilbert problem of the foundations of geometry ,”
Am. J. Math.
41 : 4
(October 1919 ),
pp. 299–319 .
MR
1506395
JFM
47.0513.02
article
BibTeX
@article {key1506395m,
AUTHOR = {Moore, R. L.},
TITLE = {On the {L}ie--{R}iemann-{H}elmholtz--{H}ilbert
problem of the foundations of geometry},
JOURNAL = {Am. J. Math.},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {41},
NUMBER = {4},
MONTH = {October},
YEAR = {1919},
PAGES = {299--319},
DOI = {10.2307/2370289},
NOTE = {MR:1506395. JFM:47.0513.02.},
ISSN = {0002-9327},
CODEN = {AJMAAN},
}
R. L. Moore :
“Concerning a set of postulates for plane analysis situs ,”
Trans. Am. Math. Soc.
20 : 2
(April 1919 ),
pp. 169–178 .
MR
1501119
JFM
47.0519.06
article
BibTeX
@article {key1501119m,
AUTHOR = {Moore, Robert L.},
TITLE = {Concerning a set of postulates for plane
analysis situs},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {20},
NUMBER = {2},
MONTH = {April},
YEAR = {1919},
PAGES = {169--178},
DOI = {10.2307/1988988},
NOTE = {MR:1501119. JFM:47.0519.06.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“Continuous sets that have no continuous sets of condensation ,”
Bull. Am. Math. Soc.
25 : 4
(1919 ),
pp. 174–176 .
MR
1560170
JFM
47.0177.03
article
Abstract
BibTeX
Janiszewski has shown [1911-12] that if \( A \) and \( B \) are two distinct points then every bounded set of points that is irreducibly continuous from \( A \) to \( B \) , and has no continuous set of condensation, is a simple continuous arc from \( A \) to \( B \) . In the present paper I will establish the following result:
Every bounded continuous set of points that has no continuous set of condensation is a continuous curve.
@article {key1560170m,
AUTHOR = {Moore, R. L.},
TITLE = {Continuous sets that have no continuous
sets of condensation},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {25},
NUMBER = {4},
YEAR = {1919},
PAGES = {174--176},
DOI = {10.1090/S0002-9904-1919-03173-5},
NOTE = {MR:1560170. JFM:47.0177.03.},
ISSN = {0002-9904},
}
R. L. Moore :
“On the most general class \( L \) of Fréchet in which the Heine–Borel–Lebesgue theorem holds true ,”
Proc. Nat. Acad. Sci. U.S.A.
5 : 6
(June 1919 ),
pp. 206–210 .
JFM
47.0896.01
article
BibTeX
@article {key47.0896.01j,
AUTHOR = {Moore, R. L.},
TITLE = {On the most general class \$L\$ of {F}r\'echet
in which the {H}eine--{B}orel--{L}ebesgue
theorem holds true},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {5},
NUMBER = {6},
MONTH = {June},
YEAR = {1919},
PAGES = {206--210},
DOI = {10.1073/pnas.5.6.206},
NOTE = {JFM:47.0896.01.},
ISSN = {0027-8424},
}
R. L. Moore and J. R. Kline :
“On the most general plane closed point-set through which it is possible to pass a simple continuous arc ,”
Ann. Math. (2)
20 : 3
(March 1919 ),
pp. 218–223 .
MR
1502556
JFM
46.0829.02
article
Abstract
People
BibTeX
In the present paper we will establish the following result: In order that a closed and bounded point-set \( M \) should be a subset of a simple continuous arc it is necessary and sufficient that every closed, connected subset of \( M \) should be either a single point or a simple continuous arc \( t \) such that no point of \( t \) , with the exception of its endpoints is a limit point of \( M-t \) .
@article {key1502556m,
AUTHOR = {Moore, R. L. and Kline, J. R.},
TITLE = {On the most general plane closed point-set
through which it is possible to pass
a simple continuous arc},
JOURNAL = {Ann. Math. (2)},
FJOURNAL = {Annals of Mathematics. Second Series},
VOLUME = {20},
NUMBER = {3},
MONTH = {March},
YEAR = {1919},
PAGES = {218--223},
DOI = {10.2307/1967872},
NOTE = {MR:1502556. JFM:46.0829.02.},
ISSN = {0003-486X},
CODEN = {ANMAAH},
}
R. L. Moore :
“Book review: ‘Projective geometry’, vol. 2 ,”
Bull. Am. Math. Soc.
26 : 9
(1920 ),
pp. 412–425 .
Book by O. Veblen and J. W. Young (Ginn & Co., 1918).
MR
1560330
JFM
47.0583.01
article
People
BibTeX
@article {key1560330m,
AUTHOR = {Moore, R. L.},
TITLE = {Book review: ``{P}rojective geometry'',
vol.~2},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {26},
NUMBER = {9},
YEAR = {1920},
PAGES = {412--425},
DOI = {10.1090/S0002-9904-1920-03332-X},
URL = {http://projecteuclid.org/euclid.bams/1183425346},
NOTE = {Book by O.~Veblen and J.~W. Young (Ginn
\& Co., 1918). MR:1560330. JFM:47.0583.01.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning simple continuous curves ,”
Trans. Am. Math. Soc.
21 : 3
(July 1920 ),
pp. 333–347 .
MR
1501148
JFM
47.0519.08
article
Abstract
BibTeX
In the present paper I will give a definition of a simple continuous arc which stipulates neither that the set \( M \) should be bounded nor that it should contain no proper connected subset containing both \( A \) and \( B \) . I will show that, in a euclidean space of two dimensions, every point-set that satisfies this definition is an arc in the sense of Jordan.
@article {key1501148m,
AUTHOR = {Moore, Robert L.},
TITLE = {Concerning simple continuous curves},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {21},
NUMBER = {3},
MONTH = {July},
YEAR = {1920},
PAGES = {333--347},
DOI = {10.2307/1988935},
NOTE = {MR:1501148. JFM:47.0519.08.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“Concerning certain equicontinuous systems of curves ,”
Trans. Am. Math. Soc.
22 : 1
(January 1921 ),
pp. 41–55 .
MR
1501158
JFM
48.0661.01
article
BibTeX
@article {key1501158m,
AUTHOR = {Moore, Robert L.},
TITLE = {Concerning certain equicontinuous systems
of curves},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {22},
NUMBER = {1},
MONTH = {January},
YEAR = {1921},
PAGES = {41--55},
DOI = {10.2307/1988841},
NOTE = {MR:1501158. JFM:48.0661.01.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“Conditions under which one of two given closed linear point sets may be thrown into the other by continous transformation of a plane into itself ,”
Bull. Am. Math. Soc.
27 : 7
(1921 ),
pp. 297–298 .
Abstract only.
Article in Am. J. Math. 48 :1 (1926) .
JFM
48.0666.05
article
BibTeX
@article {key48.0666.05j,
AUTHOR = {Moore, R. L.},
TITLE = {Conditions under which one of two given
closed linear point sets may be thrown
into the other by continous transformation
of a plane into itself},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {27},
NUMBER = {7},
YEAR = {1921},
PAGES = {297--298},
URL = {http://www.ams.org/journals/bull/1921-27-07/S0002-9904-1921-03424-0/S0002-9904-1921-03424-0.pdf},
NOTE = {Abstract only. Article in \textit{Am.
J. Math.} \textbf{48}:1 (1926). JFM:48.0666.05.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning continuous curves in the plane ,”
Math. Z.
15 : 1
(1922 ),
pp. 254–260 .
MR
1544571
JFM
48.0660.01
article
Abstract
BibTeX
@article {key1544571m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning continuous curves in the
plane},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {15},
NUMBER = {1},
YEAR = {1922},
PAGES = {254--260},
DOI = {10.1007/BF01494397},
NOTE = {MR:1544571. JFM:48.0660.01.},
ISSN = {0025-5874},
CODEN = {MAZEAX},
}
R. L. Moore :
“Concerning connectedness im kleinen and a related property ,”
Fund. Math.
3
(1922 ),
pp. 232–237 .
JFM
48.0659.03
article
Abstract
BibTeX
Sierpiński has recently shown [1920] that in order that a closed and connected set of points \( M \) should be a continuous curve it is necessary and sufficient that, for every positive number \( \varepsilon \) , the point-set \( M \) should be the sum of a finite number of closed and connected point-sets each of diameter less than \( \varepsilon \) . It follows that, as applied to point-sets which are closed, bounded and connnected , this property is equivalent to that of connectedness im kleinen. In the present paper I will make a further study of these two properties (or rather of suitable modifications of these properties) especially as applied to sets which are not necessarily closed.
@article {key48.0659.03j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning connectedness im kleinen
and a related property},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {3},
YEAR = {1922},
PAGES = {232--237},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm3/fm3123.pdf},
NOTE = {JFM:48.0659.03.},
ISSN = {0016-2736},
}
R. L. Moore :
“On the relation of a continuous curve to its complementary domains in space of three dimensions ,”
Proc. Nat. Acad. Sci. U.S.A.
8 : 3
(March 1922 ),
pp. 33–38 .
JFM
48.0660.02
article
Abstract
BibTeX
Schoenflies has shown [1908, p. 237] that, in order that a closed, bounded and connected point-set, lying in a plane \( S \) , should be a continuous curve, it is necessary and sufficient that
if \( R \) is a domain complementary to \( M \) , every point of the boundary of \( R \) should be “accessible from all sides” with respect to \( R \) , and
if \( \varepsilon \) is any preassigned positive number, there do not exist infinitely many distinct domains, complementary to \( M \) , and all of diameter greater than \( \varepsilon \) .
In the present paper I will exhibit examples of continuous curves, in space of three dimensions, which satisfy neither of these conditions.
@article {key48.0660.02j,
AUTHOR = {Moore, R. L.},
TITLE = {On the relation of a continuous curve
to its complementary domains in space
of three dimensions},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {8},
NUMBER = {3},
MONTH = {March},
YEAR = {1922},
PAGES = {33--38},
DOI = {10.1073/pnas.8.3.33},
NOTE = {JFM:48.0660.02.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning relatively uniform convergence ,”
Bull. Am. Math. Soc.
28 : 6
(1922 ),
pp. 293 .
Abstract only.
Article in Bull. Am. Math. Soc. 30 :9–10 (1924) .
JFM
48.0299.05
article
Abstract
BibTeX
According to E. H. Moore, a sequence of functions \( f_1(p) \) , \( f_2(p) \) , \( f_3(p),\dots \) , defined on a range \( K \) , is said to converge, to a function \( f(p) \) , relatively uniformly with respect to the scale function \( s(p) \) if, for every positive number \( e \) , there exists a positive number \( \delta_e \) such that if \( n > \delta_e \) then, for every \( p \) which belongs to \( K \) ,
\[ |f_n(p)-f(p)| < e|s(p)| .\]
In this note I will establish the following theorem: If \( S \) is a convergent sequence of measurable functions \( f_1(x) \) , \( f_2(x) \) , \( f_3(x),\dots \) defined on a measurable point set \( E \) and \( S \) converges for each \( x \) belonging to \( E \) , then \( E \) contains a subset \( E_0 \) of measure zero such that the sequence \( S \) converges relatively uniformly for all values of \( x \) on the range \( E-E_0 \) .
@article {key48.0299.05j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning relatively uniform convergence},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {28},
NUMBER = {6},
YEAR = {1922},
PAGES = {293},
URL = {http://www.ams.org/journals/bull/1922-28-06/S0002-9904-1922-03567-7/S0002-9904-1922-03567-7.pdf},
NOTE = {Abstract only. Article in \textit{Bull.
Am. Math. Soc.} \textbf{30}:9--10 (1924).
JFM:48.0299.05.},
ISSN = {0002-9904},
}
R. L. Moore :
“Report on continuous curves from the viewpoint of analysis situs ,”
Bull. Am. Math. Soc.
29 : 7
(1923 ),
pp. 289–302 .
MR
1560734
JFM
49.0401.03
article
BibTeX
@article {key1560734m,
AUTHOR = {Moore, R. L.},
TITLE = {Report on continuous curves from the
viewpoint of analysis situs},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {29},
NUMBER = {7},
YEAR = {1923},
PAGES = {289--302},
DOI = {10.1090/S0002-9904-1923-03724-5},
NOTE = {MR:1560734. JFM:49.0401.03.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning the cut-points of continuous curves and of other closed and connected point-sets ,”
Proc. Nat. Acad. Sci. U.S.A.
9 : 4
(April 1923 ),
pp. 101–106 .
JFM
49.0143.01
article
BibTeX
@article {key49.0143.01j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the cut-points of continuous
curves and of other closed and connected
point-sets},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {9},
NUMBER = {4},
MONTH = {April},
YEAR = {1923},
PAGES = {101--106},
DOI = {10.1073/pnas.9.4.101},
NOTE = {JFM:49.0143.01.},
ISSN = {0027-8424},
}
R. L. Moore :
“On the generation of a simple surface by means of a set of equicontinuous curves ,”
Fund. Math.
4
(1923 ),
pp. 106–117 .
JFM
49.0402.01
article
BibTeX
@article {key49.0402.01j,
AUTHOR = {Moore, R. L.},
TITLE = {On the generation of a simple surface
by means of a set of equicontinuous
curves},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {4},
YEAR = {1923},
PAGES = {106--117},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm4/fm417.pdf},
NOTE = {JFM:49.0402.01.},
ISSN = {0016-2736},
}
R. L. Moore :
“An uncountable, closed, and non-dense point set each of whose complementary intervals abuts on another one at each of its ends ,”
Bull. Am. Math. Soc.
29 : 2
(1923 ),
pp. 49–50 .
MR
1560661
JFM
49.0142.04
article
BibTeX
@article {key1560661m,
AUTHOR = {Moore, R. L.},
TITLE = {An uncountable, closed, and non-dense
point set each of whose complementary
intervals abuts on another one at each
of its ends},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {29},
NUMBER = {2},
YEAR = {1923},
PAGES = {49--50},
DOI = {10.1090/S0002-9904-1923-03657-4},
NOTE = {MR:1560661. JFM:49.0142.04.},
ISSN = {0002-9904},
}
R. L. Moore :
“A connected and regular point set which contains no arc ,”
Bull. Am. Math. Soc.
29 : 10
(1923 ),
pp. 438 .
Abstract only.
Article in Bull. Am. Math. Soc. 32 :4 (1926) .
JFM
49.0412.16
article
BibTeX
@article {key49.0412.16j,
AUTHOR = {Moore, R. L.},
TITLE = {A connected and regular point set which
contains no arc},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {29},
NUMBER = {10},
YEAR = {1923},
PAGES = {438},
URL = {http://www.ams.org/journals/bull/1923-29-10/S0002-9904-1923-03790-7/S0002-9904-1923-03790-7.pdf},
NOTE = {Abstract only. Article in \textit{Bull.
Am. Math. Soc.} \textbf{32}:4 (1926).
JFM:49.0412.16.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning the sum of a countable number of mutually exclusive continua in the plane ,”
Fund. Math.
6
(1924 ),
pp. 189–202 .
JFM
50.0137.04
article
Abstract
BibTeX
In [1918], Sierpiński showed that if the sum of a countably infinite collection of closed point sets is bounded then it is not a continuum. He raised the question whether this theorem remains true if the restriction that the sum should be bounded is removed from the hypothesis. It will be shown, in the present paper, that, for the case where each point set of the collection in question is itself a continuum , this question may be answered in the affirmative.
@article {key50.0137.04j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the sum of a countable number
of mutually exclusive continua in the
plane},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {6},
YEAR = {1924},
PAGES = {189--202},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm6/fm6121.pdf},
NOTE = {JFM:50.0137.04.},
ISSN = {0016-2736},
}
R. L. Moore :
“An extension of the theorem that no countable point set is perfect ,”
Proc. Nat. Acad. Sci. U.S.A.
10 : 5
(May 1924 ),
pp. 168–170 .
JFM
50.0130.01
article
Abstract
BibTeX
Sierpinski [1918] showed that if a bounded and closed point set is the sum of a countable number of mutually exclusive closed point sets then it is not connected. In the present paper I will prove the following: If a bounded and closed point set is the sum of a countable number of mutually exclusive closed and connected point sets \( M_1 \) , \( M_2 \) , \( M_3,\dots \) then not every point set of this sequence contains a limit point of the sum of the remaining ones.
@article {key50.0130.01j,
AUTHOR = {Moore, R. L.},
TITLE = {An extension of the theorem that no
countable point set is perfect},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {10},
NUMBER = {5},
MONTH = {May},
YEAR = {1924},
PAGES = {168--170},
DOI = {10.1073/pnas.10.5.168},
NOTE = {JFM:50.0130.01.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning upper semi-continuous collections of continua which do not separate a given continuum ,”
Proc. Nat. Acad. Sci. U.S.A.
10 : 8
(August 1924 ),
pp. 356–360 .
An abstract was published in Bull. Am. Math. Soc. 31 :3 (1925) .
JFM
50.0130.04
article
Abstract
BibTeX
In her thesis [1922], Miss Anna M. Mullikin showed that if \( M \) is the set ofall points in a given plane and \( G \) is a countable collection of mutually exclusive closed subsets of \( M \) no one of which disconnects \( M \) then \( M \) is not disconnected by the sum of all the point sets of the collection \( G \) . It is clear that this proposition does not remain true if the phrase “\( M \) is the set of all points in a given plane” is replaced by the phrase “\( M \) is a closed and connected subset of the set \( S \) of all the points of a given plane.” If \( M \) is any simple closed curve, \( A \) and \( B \) are two points belonging to \( M \) and the point sets of the collection \( G \) are the points \( A \) and \( B \) then no point set of the collection \( G \) separates \( M \) , but their sum does separate \( M \) . It is to be observed that in this case \( M \) disconnects \( S \) .
@article {key50.0130.04j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning upper semi-continuous collections
of continua which do not separate a
given continuum},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {10},
NUMBER = {8},
MONTH = {August},
YEAR = {1924},
PAGES = {356--360},
DOI = {10.1073/pnas.10.8.356},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{31}:3 (1925).
JFM:50.0130.04.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning the common boundary of two domains ,”
Fund. Math.
6
(1924 ),
pp. 203–213 .
JFM
50.0138.04
article
Abstract
BibTeX
In an article [1924] published in Volume 5 of this journal, J. R. Kline has shown that in order that a bounded continuum should be a simple closed curve it is necessary and sufficient that it should remain connected (in the weak sense) on the removal of any one of its connected proper subsets. In the same volume C. Kuratowski [1924] has shown that in order that a bounded continuum should be a simple closed curve it is necessary and sufficient that it should remain connected in the strong sense on the removal of any one of its connected proper sets which is closed . In the present paper I will show, among other things, that if a bounded continuum has more than one prime part and no one of its prime parts separates the plane then in order that it should have just two complementary domains and be the complete boundary of each of them it is necessary and sufficient that it should remain connected in the weak sense on the removal of any one of its connected proper subsets which is closed .
@article {key50.0138.04j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the common boundary of two
domains},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {6},
YEAR = {1924},
PAGES = {203--213},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm6/fm6122.pdf},
NOTE = {JFM:50.0138.04.},
ISSN = {0016-2736},
}
R. L. Moore :
“Concerning relatively uniform convergence ,”
Bull. Am. Math. Soc.
30 : 9–10
(1924 ),
pp. 504–505 .
An abstract was published in Bull. Am. Math. Soc. 28 :6 (1922) .
MR
1560954
JFM
50.0179.01
article
Abstract
BibTeX
According to E. H. Moore, a sequence of functions \( f_1(p) \) , \( f_2(p) \) , \( f_3(p),\dots \) , defined on a range \( K \) , is said to converge, to a function \( f(p) \) , relatively uniformly with respect to the scale function \( s(p) \) if, for every positive number \( e \) , there exists a positive number \( \delta_e \) such that if \( n > \delta_e \) then, for every \( p \) which belongs to \( K \) ,
\[ |f_n(p)-f(p)| < e|s(p)| .\]
In this note I will establish the following theorem: If \( S \) is a convergent sequence of measurable functions \( f_1(x) \) , \( f_2(x) \) , \( f_3(x),\dots \) defined on a measurable point set \( E \) and \( S \) converges for each \( x \) belonging to \( E \) , then \( E \) contains a subset \( E_0 \) of measure zero such that the sequence \( S \) converges relatively uniformly for all values of \( x \) on the range \( E-E_0 \) .
@article {key1560954m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning relatively uniform convergence},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {30},
NUMBER = {9--10},
YEAR = {1924},
PAGES = {504--505},
DOI = {10.1090/S0002-9904-1924-03945-7},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{28}:6 (1922).
MR:1560954. JFM:50.0179.01.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning sets of segments which cover a point set in the Vitali sense ,”
Proc. Nat. Acad. Sci. U.S.A.
10 : 11
(November 1924 ),
pp. 464–467 .
An abstract was published in Bull. Am. Math. Soc. 31 :3 (1925) .
JFM
50.0131.01
article
Abstract
BibTeX
A set of segments \( G \) will be said to cover a point set \( K \) in the Vitali sense if, for every point \( P \) which belongs to \( K \) and every positive number \( e \) , there exists a segment of \( G \) which contains \( P \) and is of length less than \( e \) . In a recent paper [1924] J. Spława-Neyman has shown that if, in space of one dimension, \( K \) is a closed and bounded point set of measure zero and \( G \) is a set of segments which covers \( K \) in the Vitali sense then for every positive number \( e \) the set \( G \) contains a subject \( G_e \) , such that \( G_e \) , covers \( K \) and such that the sum of the lengths of all the segments of the set \( G_e \) is less than \( e \) . He indicates that Sierpinski has raised the question whether this theorem remains true if the stipulation that \( K \) be closed is omitted. I will show that this question may be answered in the negative.
@article {key50.0131.01j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning sets of segments which cover
a point set in the {V}itali sense},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {10},
NUMBER = {11},
MONTH = {November},
YEAR = {1924},
PAGES = {464--467},
DOI = {10.1073/pnas.10.11.464},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{31}:3 (1925).
JFM:50.0131.01.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning the prime parts of certain continua which separate the plane ,”
Proc. Nat. Acad. Sci. U.S.A.
10 : 5
(May 1924 ),
pp. 170–175 .
JFM
50.0130.02
article
Abstract
BibTeX
If, in a plane \( S \) , \( M \) is a bounded continuum which has more than one prime part and no prime part of \( M \) separates \( S \) , then, in order that \( S-M \) shall be the sum of two mutually exclusive domains such that each prime part of \( M \) contains at least one limit point of each of these domains, it is necessary and sufficient that the set whose elements are the prime parts of \( M \) shall be a simple closed curve of prime parts in the sense that it is disconnected by the omission of any two of its elements which are not identical.
@article {key50.0130.02j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the prime parts of certain
continua which separate the plane},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {10},
NUMBER = {5},
MONTH = {May},
YEAR = {1924},
PAGES = {170--175},
DOI = {10.1073/pnas.10.5.170},
NOTE = {JFM:50.0130.02.},
ISSN = {0027-8424},
}
R. L. Moore :
“A characterization of a continuous curve ,”
Bull. Am. Math. Soc.
30 : 9
(1924 ),
pp. 484 .
Abstract only.
Article in Fund. Math. 7 (1925) .
JFM
50.0374.07
article
BibTeX
@article {key50.0374.07j,
AUTHOR = {Moore, R. L.},
TITLE = {A characterization of a continuous curve},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {30},
NUMBER = {9},
YEAR = {1924},
PAGES = {484},
URL = {http://www.ams.org/journals/bull/1924-30-09/S0002-9904-1924-03937-8/S0002-9904-1924-03937-8.pdf},
NOTE = {Abstract only. Article in \textit{Fund.
Math.} \textbf{7} (1925). JFM:50.0374.07.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning upper semi-continuous collections of continua ,”
Trans. Am. Math. Soc.
27 : 4
(October 1925 ),
pp. 416–428 .
MR
1501320
JFM
51.0464.03
article
BibTeX
@article {key1501320m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning upper semi-continuous collections
of continua},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {27},
NUMBER = {4},
MONTH = {October},
YEAR = {1925},
PAGES = {416--428},
DOI = {10.2307/1989234},
NOTE = {MR:1501320. JFM:51.0464.03.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“Concerning the separation of point sets by curves ,”
Proc. Nat. Acad. Sci. U.S.A.
11 : 8
(August 1925 ),
pp. 469–476 .
An abstract was published in Bull. Am. Math. Soc. 32 :1 (1926) .
JFM
51.0459.04
article
Abstract
BibTeX
It has been shown by Zoretti [1905] that if \( K \) is a bounded maximal connected subset of a continuum \( M \) and \( e \) is a positive number then there exists a simple closed curve \( J \) which encloses \( K \) and contains no point of \( M \) and which has the further property that every one of its points is at a distance less than \( e \) from some point of \( K \) . It is to be observed that this does not imply that every point within \( J \) is at a distance less than \( e \) from some point of \( K \) . Indeed if \( K \) is, for example, a circle and \( e \) is less than its radius then there exists no \( J \) having this property.
@article {key51.0459.04j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the separation of point sets
by curves},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {11},
NUMBER = {8},
MONTH = {August},
YEAR = {1925},
PAGES = {469--476},
DOI = {10.1073/pnas.11.8.469},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{32}:1 (1926).
JFM:51.0459.04.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning the prime parts of a continuum ,”
Math. Z.
22 : 1
(1925 ),
pp. 307–315 .
MR
1544726
JFM
51.0461.02
article
Abstract
BibTeX
In his paper [1921] H. Hahn has recently introduced the notion of the prime parts of a continuum and has established a result which may be indicated as follows: If a bounded continuum which is irreducible between the points \( A \) and \( B \) , and which has more than one prime part, is considered as being composed of its prime parts, and not (unless its prime parts are all points) as merely a set of points, then, with respect to these elements, it is a simple continuous arc from \( A \) to \( B \) . In the present paper I will show, among other thigns, that every bounded continuum whatsoever which has more than one prime part is a continuous curve with respect to its prime parts.
@article {key1544726m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the prime parts of a continuum},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {22},
NUMBER = {1},
YEAR = {1925},
PAGES = {307--315},
DOI = {10.1007/BF01479609},
NOTE = {MR:1544726. JFM:51.0461.02.},
ISSN = {0025-5874},
CODEN = {MAZEAX},
}
R. L. Moore :
“A characterization of a continuous curve ,”
Fund. Math.
7
(1925 ),
pp. 302–307 .
An abstract was published in Bull. Am. Math. Soc. 30 :9 (1924) .
JFM
51.0462.04
article
Abstract
BibTeX
If \( A \) and \( B \) are points belonging to a connected point set \( M \) , a point set \( K \) is said to separate \( A \) from \( B \) in \( M \) if \( K \) is a proper subset of \( M \) and \( M - K \) is the sum of two mutually separated point sets which contain \( A \) and \( B \) respectively. It is shown that in order that a plane continuum \( M \) shall be a continuous curve it is necessary and sufficient that, for every two points \( A \) and \( B \) that belong to \( M \) , there exist a finite number of continua whose sum separates \( A \) from \( B \) in \( M \) . In order that a bounded plane continuum \( M \) shall be a continuous curve which neither contains a domain nor separates the plane, it is necessary and sufficient that, for every two distinct points \( A \) and \( B \) which belong to \( M \) , there exist a point which separates \( A \) from \( B \) in \( M \) .
@article {key51.0462.04j,
AUTHOR = {Moore, R. L.},
TITLE = {A characterization of a continuous curve},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {7},
YEAR = {1925},
PAGES = {302--307},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm7/fm7125.pdf},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{30}:9 (1924).
JFM:51.0462.04.},
ISSN = {0016-2736},
}
R. L. Moore :
“Concerning sets of segments which cover a point set in the Vitali sense ,”
Bull. Am. Math. Soc.
31 : 3
(1925 ),
pp. 120 .
Abstract only.
Article in Proc. Nat. Acad. Sci. U.S.A. 10 :11 (1924) .
JFM
51.0170.11
article
BibTeX
@article {key51.0170.11j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning sets of segments which cover
a point set in the {V}itali sense},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {31},
NUMBER = {3},
YEAR = {1925},
PAGES = {120},
URL = {http://www.ams.org/journals/bull/1925-31-03/S0002-9904-1925-03990-7/S0002-9904-1925-03990-7.pdf},
NOTE = {Abstract only. Article in \textit{Proc.
Nat. Acad. Sci. U.S.A.} \textbf{10}:11
(1924). JFM:51.0170.11.},
ISSN = {0002-9904},
}
R. L. Moore :
“Covering theorems ,”
Bull. Am. Math. Soc.
31 : 5
(1925 ),
pp. 219–220 .
Abstract only.
Article in Bull. Am. Math. Soc. 32 :3 (1926) .
JFM
51.0170.09
article
BibTeX
@article {key51.0170.09j,
AUTHOR = {Moore, R. L.},
TITLE = {Covering theorems},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {31},
NUMBER = {5},
YEAR = {1925},
PAGES = {219--220},
URL = {http://www.ams.org/journals/bull/1925-31-05/S0002-9904-1925-04035-5/S0002-9904-1925-04035-5.pdf},
NOTE = {Abstract only. Article in \textit{Bull.
Am. Math. Soc.} \textbf{32}:3 (1926).
JFM:51.0170.09.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning upper semi-continuous collections ,”
Bull. Am. Math. Soc.
31 : 5
(1925 ),
pp. 220 .
Early research report published in Monatsh. Math. Phys. 36 :1 (1929) . See also Bull. Am. Math. Soc. 34 :4 (1928) .
JFM
51.0466.10
article
BibTeX
@article {key51.0466.10j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning upper semi-continuous collections},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {31},
NUMBER = {5},
YEAR = {1925},
PAGES = {220},
URL = {http://www.ams.org/journals/bull/1925-31-05/S0002-9904-1925-04035-5/S0002-9904-1925-04035-5.pdf},
NOTE = {Early research report published in \textit{Monatsh.
Math. Phys.} \textbf{36}:1 (1929). See
also \textit{Bull. Am. Math. Soc.} \textbf{34}:4
(1928). JFM:51.0466.10.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning upper semi-continuous collections of continua which do not separate a given continuum ,”
Bull. Am. Math. Soc.
31 : 3
(1925 ),
pp. 120 .
Abstract only.
Article in Proc. Nat. Acad. Sci. U.S.A. 10 :8 (1924) .
JFM
51.0466.08
article
BibTeX
@article {key51.0466.08j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning upper semi-continuous collections
of continua which do not separate a
given continuum},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {31},
NUMBER = {3},
YEAR = {1925},
PAGES = {120},
URL = {http://www.ams.org/journals/bull/1925-31-03/S0002-9904-1925-03990-7/S0002-9904-1925-03990-7.pdf},
NOTE = {Abstract only. Article in \textit{Proc.
Nat. Acad. Sci. U.S.A.} \textbf{10}:8
(1924). JFM:51.0466.08.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning the relation between separability and the proposition that every uncountable point set has a limit point ,”
Fund. Math.
8
(1926 ),
pp. 189–192 .
An abstract was published in Bull. Am. Math. Soc. 32 :1 (1926) .
JFM
52.0583.03
article
Abstract
BibTeX
In this paper it is shown that in order that every subset of a given class \( D \) of Fréchet should be separable it is necessary and sufficient that every uncountable subclass of that class should have a limit point, and in order that this condition should be fulfilled it is necessary and sufficient that every uncountable subclass of D should contain a point of condensation of itself. It follows that a class \( D \) is separable if, and only if, every subset of it is separable.
@article {key52.0583.03j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the relation between separability
and the proposition that every uncountable
point set has a limit point},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {8},
YEAR = {1926},
PAGES = {189--192},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm8/fm8113.pdf},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{32}:1 (1926).
JFM:52.0583.03.},
ISSN = {0016-2736},
}
R. L. Moore :
“Concerning indecomposable continua and continua which contain no subsets that separate the plane ,”
Proc. Nat. Acad. Sci. U.S.A.
12 : 5
(May 1926 ),
pp. 359–363 .
JFM
52.0600.04
article
BibTeX
@article {key52.0600.04j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning indecomposable continua and
continua which contain no subsets that
separate the plane},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {12},
NUMBER = {5},
MONTH = {May},
YEAR = {1926},
PAGES = {359--363},
DOI = {10.1073/pnas.12.5.359},
NOTE = {JFM:52.0600.04.},
ISSN = {0027-8424},
}
R. L. Moore :
“Conditions under which one of two given closed linear point sets may be thrown into the other by continous transformation of a plane into itself ,”
Am. J. Math
48 : 1
(January 1926 ),
pp. 67–72 .
An abstract was published in Bull. Am. Math. Soc. 27 :7 (1921) .
MR
1506573
JFM
52.0604.03
article
Abstract
BibTeX
In this paper the following theorem will be established: If, in a plane \( S \) , \( M \) and \( N \) are two closed and bounded linear point sets and there exists a one to one continuous transformation \( T \) , with single valued inverse, which throws \( M \) into \( N \) then there exists a one to one continuous transformation of \( S \) into itself which also has a single valued inverse and which carries \( M \) into \( N \) in such a way that if \( X \) belongs to \( M \) then it is carried into \( T(X) \) .
@article {key1506573m,
AUTHOR = {Moore, R. L.},
TITLE = {Conditions under which one of two given
closed linear point sets may be thrown
into the other by continous transformation
of a plane into itself},
JOURNAL = {Am. J. Math},
FJOURNAL = {American Journal of Mathematics},
VOLUME = {48},
NUMBER = {1},
MONTH = {January},
YEAR = {1926},
PAGES = {67--72},
DOI = {10.2307/2370821},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{27}:7 (1921).
MR:1506573. JFM:52.0604.03.},
ISSN = {0002-9327},
CODEN = {AJMAAN},
}
R. L. Moore :
“Covering theorems ,”
Bull. Am. Math. Soc.
32 : 3
(1926 ),
pp. 275–282 .
An abstract was published in Bull. Am. Math. Soc. 31 :5 (1925) .
MR
1561204
JFM
52.0197.03
article
Abstract
BibTeX
Using the following definition: A point set \( K \) is said to be uniformly relatively well imbedded in a set of regions \( G \) if there exists a positive number \( d \) , less than unity, such that each point of \( K \) belongs to some region \( R \) of \( G \) and is at a distance from the boundary of \( R \) less than \( d \) times the diameter of \( R \) , the author proves these theorems: (1) If, for each circle \( g \) of a set \( G \) , \( h_g \) is a definite circle concentric with \( g \) and there exists a positive \( e \) , less than unity, such that, for every \( g \) , the radius of \( h_g \) is less than \( e \) times that of \( g \) , then the set \( G \) contains a subset such that, for each \( g \) , \( h_g \) is within one and only one circle of this subset. (2) If \( G \) is a set of circular regions and \( K \) is a point set of measure zero, and, for every positive \( e \) , \( K \) is uniformly relatively well imbedded in a subset of \( G \) whose regions are of radius less than \( e \) , then, for every positive \( \varepsilon \) , \( G \) contains a subset \( G^* \) which covers \( K \) , the sum of the areas of the regions of \( G^* \) being less than \( \varepsilon \) . (3) J. Splawa-Neyman’s theorem [1924] remains true if the words “à son intérieur” are omitted.
@article {key1561204m,
AUTHOR = {Moore, R. L.},
TITLE = {Covering theorems},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {32},
NUMBER = {3},
YEAR = {1926},
PAGES = {275--282},
DOI = {10.1090/S0002-9904-1926-04207-5},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{31}:5 (1925).
MR:1561204. JFM:52.0197.03.},
ISSN = {0002-9904},
}
R. L. Moore :
“A connected and regular point set which contains no arc ,”
Bull. Am. Math. Soc.
32 : 4
(1926 ),
pp. 331–332 .
An abstract was published in Bull. Am. Math. Soc. 29 :10 (1923) .
MR
1561220
JFM
52.0600.03
article
Abstract
BibTeX
@article {key1561220m,
AUTHOR = {Moore, R. L.},
TITLE = {A connected and regular point set which
contains no arc},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {32},
NUMBER = {4},
YEAR = {1926},
PAGES = {331--332},
DOI = {10.1090/S0002-9904-1926-04210-5},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{29}:10 (1923).
MR:1561220. JFM:52.0600.03.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning paths that do not separate a given continuous curve ,”
Proc. Nat. Acad. Sci. U.S.A.
12 : 12
(December 1926 ),
pp. 745–753 .
JFM
52.0603.03
article
Abstract
BibTeX
In this paper it will be shown that, in space of two dimensions, every two points that do not belong to a given continuous curve may be joined by a simple continuous arc that does not disconnect that curve.
@article {key52.0603.03j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning paths that do not separate
a given continuous curve},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {12},
NUMBER = {12},
MONTH = {December},
YEAR = {1926},
PAGES = {745--753},
DOI = {10.1073/pnas.12.12.745},
NOTE = {JFM:52.0603.03.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning the relation between separability and the proposition that every uncountable point set has a limit point ,”
Bull. Am. Math. Soc.
32 : 1
(1926 ),
pp. 13 .
Abstract only.
Article in Fund. Math. 8 (1926) .
JFM
52.0605.14
article
BibTeX
@article {key52.0605.14j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the relation between separability
and the proposition that every uncountable
point set has a limit point},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {32},
NUMBER = {1},
YEAR = {1926},
PAGES = {13},
URL = {http://www.ams.org/journals/bull/1926-32-01/S0002-9904-1926-04152-5/S0002-9904-1926-04152-5.pdf},
NOTE = {Abstract only. Article in \textit{Fund.
Math.} \textbf{8} (1926). JFM:52.0605.14.},
ISSN = {0002-9904},
}
R. L. Moore :
“Some separation theorems ,”
Proc. Nat. Acad. Sci. U.S.A.
13 : 10
(October 1927 ),
pp. 711–716 .
JFM
53.0564.02
article
Abstract
BibTeX
@article {key53.0564.02j,
AUTHOR = {Moore, R. L.},
TITLE = {Some separation theorems},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {13},
NUMBER = {10},
MONTH = {October},
YEAR = {1927},
PAGES = {711--716},
DOI = {10.1073/pnas.13.10.711},
NOTE = {JFM:53.0564.02.},
ISSN = {0027-8424},
}
R. L. Moore :
“A separation theorem ,”
Bull. Am. Math. Soc.
33 : 6
(1927 ),
pp. 656 .
Abstract only.
Article in Fund. Math. 12 (1928) .
JFM
53.0574.06
article
BibTeX
@article {key53.0574.06j,
AUTHOR = {Moore, R. L.},
TITLE = {A separation theorem},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {33},
NUMBER = {6},
YEAR = {1927},
PAGES = {656},
URL = {http://www.ams.org/journals/bull/1927-33-06/S0002-9904-1927-04440-8/S0002-9904-1927-04440-8.pdf},
NOTE = {Abstract only. Article in \textit{Fund.
Math.} \textbf{12} (1928). JFM:53.0574.06.},
ISSN = {0002-9904},
}
R. L. Moore :
“On the separation of the plane by a continuum ,”
Bull. Am. Math. Soc.
34 : 3
(1928 ),
pp. 303–306 .
MR
1561553
JFM
54.0630.02
article
Abstract
BibTeX
In his paper [1927], W. A. Wilson obtains the following theorem. Let \( F \) be the union of two bounded continua \( H_1 \) and \( H_2 \) having these properties:
\( H_1 \) and \( H_2 \) are irreducible about \( A+B \) ;
\( H_1\cdot H_2 = A+B \) where \( A \) and \( B \) are continua and \( A\cdot B = 0 \) ;
\( H_1 \) and \( H_2 \) contain subcontinua \( C_1 \) and \( C_2 \) respectively such that
\[ \alpha = C_1\cdot C_2\cdot A \neq 0, \qquad \beta = C_1\cdot C_2\cdot B\neq 0 ,\]
\( C_1 \) and \( C_2 \) are irreducible between \( \alpha \) and \( \beta \) , and \( F = C_1 + C_2 \) .
Then \( F \) cuts the plane and is the frontier of exatly two components of its complement. In the present paper I will establish two theorems which together yield more information than Wilson’s theorem.
@article {key1561553m,
AUTHOR = {Moore, R. L.},
TITLE = {On the separation of the plane by a
continuum},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {34},
NUMBER = {3},
YEAR = {1928},
PAGES = {303--306},
URL = {http://projecteuclid.org/euclid.bams/1183492728},
NOTE = {MR:1561553. JFM:54.0630.02.},
ISSN = {0002-9904},
}
R. L. Moore :
“A separation theorem ,”
Fund. Math.
12
(1928 ),
pp. 295–297 .
An abstract was published in Bull. Am. Math. Soc. 33 :6 (1927) .
JFM
54.0630.01
article
Abstract
BibTeX
In this paper the following theorems are proved. (I) If, in a plane \( S \) , \( M \) is a bounded continuous curve, \( K \) is a closed subset of \( M \) , and \( H \) is a subset of \( K \) and of some connected subset of \( K + (S - M) \) but no point set of which \( H \) is a proper subset satisfies these conditions, then if the continuum \( E \) is a subset of \( K - H \) , there exists a simple closed curve lying wholly in \( M - K \) and separating \( H \) from \( E \) . (II) If, in a plane \( S \) , \( K \) is a closed subset of a continuous curve \( M \) , and \( A \) and \( B \) are two points of \( M \) , then if \( A \) and \( B \) lie in a connected subset of \( K + (S - M) \) they lie in a closed and connected subset of \( K + (S - M) \) . (III) In order that a bounded continuum \( M \) in a plane \( S \) should be a continuous curve, it is necessary and sufficient that if \( t \) is an arc and \( H \) is an open subset of \( M + t \) , and \( A \) and \( B \) are points of \( S - H \) which are weakly separated by \( H \) , then \( H \) contains a simple closed curve that separates \( A \) from \( B \) . The first of these theorems may be regarded as an extension of a theorem of Zoretti’s.
@article {key54.0630.01j,
AUTHOR = {Moore, R. L.},
TITLE = {A separation theorem},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {12},
YEAR = {1928},
PAGES = {295--297},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{33}:6 (1927).
JFM:54.0630.01.},
ISSN = {0016-2736},
}
R. L. Moore :
“Concerning triods in the plane and the junction points of plane continua ,”
Proc. Nat. Acad. Sci. U.S.A.
14 : 1
(January 1928 ),
pp. 85–88 .
An abstract was published in Bull. Am. Math. Soc. 34 :2 (1928) .
JFM
54.0630.03
article
Abstract
BibTeX
In the present paper I shall introduce the notion junction point of a continuum and shall establish the theorem that no plane continuum whatsoever has more than a countable number of junction points. In the presence of the easily verified fact that every point of ramification of a regular curve of finite connectivity is also a junction point of that curve, the above-mentioned results of the authors cited are (insofar as they apply to the plane) special cases of this much more general theorem.
@article {key54.0630.03j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning triods in the plane and the
junction points of plane continua},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {14},
NUMBER = {1},
MONTH = {January},
YEAR = {1928},
PAGES = {85--88},
DOI = {10.1073/pnas.14.1.85},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{34}:2 (1928).
JFM:54.0630.03.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning upper semi-continuous collections ,”
Bull. Am. Math. Soc.
34 : 4
(1928 ),
pp. 416–417 .
Abstract only.
Article published in Monatsh. Math. Phys. 36 :1 (1929) . See also Bull. Am. Math. Soc. 31 :5 (1925) .
JFM
54.0645.07
article
BibTeX
@article {key54.0645.07j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning upper semi-continuous collections},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {34},
NUMBER = {4},
YEAR = {1928},
PAGES = {416--417},
URL = {http://www.ams.org/journals/bull/1928-34-04/S0002-9904-1928-04552-4/S0002-9904-1928-04552-4.pdf},
NOTE = {Abstract only. Article published in
\textit{Monatsh. Math. Phys.} \textbf{36}:1
(1929). See also \textit{Bull. Am. Math.
Soc.} \textbf{31}:5 (1925). JFM:54.0645.07.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning triods in the plane and the junction points of plane continua ,”
Bull. Am. Math. Soc.
34 : 2
(1928 ),
pp. 137 .
Abstract only.
Article in Proc. Nat. Acad. Sci. U.S.A. 14 :1 (1928) .
JFM
54.0645.04
article
BibTeX
@article {key54.0645.04j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning triods in the plane and the
junction points of plane continua},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {34},
NUMBER = {2},
YEAR = {1928},
PAGES = {137},
URL = {http://www.ams.org/journals/bull/1928-34-02/S0002-9904-1928-04500-7/S0002-9904-1928-04500-7.pdf},
NOTE = {Abstract only. Article in \textit{Proc.
Nat. Acad. Sci. U.S.A.} \textbf{14}:1
(1928). JFM:54.0645.04.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning upper semi-continuous collections ,”
Monatshefte für Mathematik und Physick
36 : 1
(1929 ),
pp. 81–88 .
An abstract was published in Bull. Am. Math. Soc. 34 :4 (1928) and an early research report in Bull. Am. Math. Soc. 31 :5 (1925) .
MR
1549673
JFM
55.0317.04
article
Abstract
BibTeX
I have shown [1925] that if, in a plane \( S \) , \( G \) is an upper semi-continuous collection of mutually exclusive compact continua and no continuum of the collection \( G \) separates \( S \) and every point of \( S \) belongs to some continuum of \( G \) then the collection \( G \) is, with reference to a suitably defined notion of limit element, topologically equivalent to a plane. It follows, in an obvious manner, that the same proposition holds true if the word plane is replaced throughout by sphere. In the present paper I will consider the situation obtained on the removal of the restriction than no continuum of the set \( G \) shall separate \( S \) .
@article {key1549673m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning upper semi-continuous collections},
JOURNAL = {Monatshefte f\"ur Mathematik und Physick},
FJOURNAL = {Monatsh. Math. Phys.},
VOLUME = {36},
NUMBER = {1},
YEAR = {1929},
PAGES = {81--88},
DOI = {10.1007/BF02307605},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{34}:4 (1928)
and an early research report in \textit{Bull.
Am. Math. Soc.} \textbf{31}:5 (1925).
MR:1549673. JFM:55.0317.04.},
ISSN = {0026-9255},
}
R. L. Moore :
“Concerning triodic continua in the plane ,”
Fund. Math.
13
(1929 ),
pp. 261–263 .
JFM
55.0978.03
article
Abstract
BibTeX
In a recent paper [1928] I defined the term triod and showed that there does not exist, in the plane, an uncountable set of mutually exclusive triods. In the present paper I will generalize this notion and establish a correspondingly more general theorem.
@article {key55.0978.03j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning triodic continua in the plane},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {13},
YEAR = {1929},
PAGES = {261--263},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm13/fm13119.pdf},
NOTE = {JFM:55.0978.03.},
ISSN = {0016-2736},
}
R. L. Moore :
Foundations of point set theory .
AMS Colloquium Publications 13 .
American Mathematical Society (Providence, RI ),
1932 .
Revised and enlarged edition published in 1962 .
JFM
58.0637.02
Zbl
0005.05403
book
BibTeX
@book {key0005.05403z,
AUTHOR = {Moore, R. L.},
TITLE = {Foundations of point set theory},
SERIES = {AMS Colloquium Publications},
NUMBER = {13},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1932},
PAGES = {vii+486},
NOTE = {Revised and enlarged edition published
in 1962. Zbl:0005.05403. JFM:58.0637.02.},
}
R. L. Moore :
“Concerning compact continua which contain no continuum that separates the plane ,”
Bull. Am. Math. Soc.
39 : 9
(1933 ),
pp. 671 .
Abstract only.
Article in Proc. Nat. Acad. Sci. U.S.A. 20 :1 (1934) .
JFM
59.0579.16
article
BibTeX
@article {key59.0579.16j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning compact continua which contain
no continuum that separates the plane},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {39},
NUMBER = {9},
YEAR = {1933},
PAGES = {671},
URL = {http://www.ams.org/journals/bull/1933-39-09/S0002-9904-1933-05718-X/S0002-9904-1933-05718-X.pdf},
NOTE = {Abstract only. Article in \textit{Proc.
Nat. Acad. Sci. U.S.A.} \textbf{20}:1
(1934). JFM:59.0579.16.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning compact continua which contain no continuum that separates the plane ,”
Proc. Nat. Acad. Sci. U.S.A.
20 : 1
(January 1934 ),
pp. 41–45 .
An abstract was published in Bull. Am. Math. Soc. 39 :9 (1933) .
Zbl
0008.32603
article
Abstract
BibTeX
It has been shown, by Mazurkiewicz [1921], that every arc which lies in a compact acyclic continuous curve \( M \) is a subset of an arc which lies in \( M \) but which is itself not a proper subset of any other such arc. In the present paper it will be shown that if, in a plane \( \alpha \) , \( S \) is a compact continuum containing no continuum that separates \( \alpha \) and \( K \) is a subcontinuum of \( S \) which is irreducible between some two points, then \( K \) is a subset of some subcontinuum of \( S \) which is irreducible between some two points but which is itself not a proper subset of any other such subcontinuum of \( S \) . With the aid of this result it will be proved that if, in the plane \( \alpha \) , \( M \) is a non-degenerate, compact and atriodic continuum which does not separate \( \alpha \) , then \( M \) is irreducible between some two points.
@article {key0008.32603z,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning compact continua which contain
no continuum that separates the plane},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {20},
NUMBER = {1},
MONTH = {January},
YEAR = {1934},
PAGES = {41--45},
DOI = {10.1073/pnas.20.1.41},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{39}:9 (1933).
Zbl:0008.32603.},
ISSN = {0027-8424},
}
R. L. Moore :
“A set of axioms for plane analysis situs ,”
Fund. Math.
25
(1935 ),
pp. 13–28 .
JFM
61.0638.04
Zbl
0011.27501
article
BibTeX
@article {key0011.27501z,
AUTHOR = {Moore, R. L.},
TITLE = {A set of axioms for plane analysis situs},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {25},
YEAR = {1935},
PAGES = {13--28},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm25/fm2514.pdf},
NOTE = {Zbl:0011.27501. JFM:61.0638.04.},
ISSN = {0016-2736},
}
R. L. Moore :
Fundamental theorems concerning point sets .
The Rice Institute Pamphlet 23 .
January 1936 .
An elaboration and extension of material presented in a series of three lectures delivered at the Rice Institute.
JFM
62.1412.03
booklet
BibTeX
@booklet {key62.1412.03j,
AUTHOR = {Moore, R. L.},
TITLE = {Fundamental theorems concerning point
sets},
SERIES = {The Rice Institute Pamphlet},
NUMBER = {23},
MONTH = {January},
YEAR = {1936},
PAGES = {1--74},
NOTE = {An elaboration and extension of material
presented in a series of three lectures
delivered at the Rice Institute. JFM:62.1412.03.},
}
R. L. Moore :
“Concerning essential continua of condensation ,”
Bull. Am. Math. Soc.
42 : 1
(1936 ),
pp. 35–36 .
Abstact only.
Article in Trans. Am. Math. Soc. 42 :1 (1936) .
JFM
62.0696.08
article
BibTeX
@article {key62.0696.08j,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning essential continua of condensation},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {42},
NUMBER = {1},
YEAR = {1936},
PAGES = {35--36},
URL = {http://www.ams.org/journals/bull/1936-42-01/S0002-9904-1936-06249-X/S0002-9904-1936-06249-X.pdf},
NOTE = {Abstact only. Article in \textit{Trans.
Am. Math. Soc.} \textbf{42}:1 (1936).
JFM:62.0696.08.},
ISSN = {0002-9904},
}
R. L. Moore :
“Concerning essential continua of condensation ,”
Trans. Am. Math. Soc.
42 : 1
(July 1937 ),
pp. 41–52 .
An abstract was published in Bull. Am. Math. Soc. 42 :1 (1936) .
MR
1501913
JFM
63.1165.03
Zbl
0017.09201
article
Abstract
BibTeX
The continuum \( M \) is said to have property \( N \) if for every positive number \( e \) there exists a finite set \( H \) of non-degenerate subcontinua of \( M \) such that every subcontinuum of \( M \) of diameter more than \( e \) contains some continuum of \( H \) . The author has shown (see a forthcoming issue of the Rice Institute Pamphlet [1936]) that no compact continuum with property \( N \) has an essential continuum of condensation. It is now shown that if the compact and webless continuum \( M \) does not have property \( N \) there exists an upper semi-continuous collection of mutually exclusive continua filling up \( M \) and forming, with respect to its elements, a continuum with an essential continuum of condensation. In order that the compact and webless continuum \( M \) should have no essential continuum of condensation it is necessary and sufficient that every non-degenerate subcontinuum of \( M \) should contain uncountably many local separating points of \( M \) . In order that such a continuum should have an essential continuum of condensation it is necessary and sufficient that there should exist a positive number \( d \) such that if \( G is an upper semi-continuous collection of mutually exclusive continua filling up \) M\( and forming, with respect to its elements, a continuum with no continuum of condensation, then some continuum of \) G\( is of diameter more than \) d\( . \)
@article {key1501913m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning essential continua of condensation},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {42},
NUMBER = {1},
MONTH = {July},
YEAR = {1937},
PAGES = {41--52},
DOI = {10.2307/1989674},
NOTE = {An abstract was published in \textit{Bull.
Am. Math. Soc.} \textbf{42}:1 (1936).
MR:1501913. Zbl:0017.09201. JFM:63.1165.03.},
ISSN = {0002-9947},
CODEN = {TAMTAM},
}
R. L. Moore :
“Concerning accessibility ,”
Proc. Nat. Acad. Sci. U.S.A.
25 : 12
(1 1939 ),
pp. 648–653 .
MR
0000643
JFM
65.0874.01
Zbl
0023.11401
article
BibTeX
@article {key0000643m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning accessibility},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {25},
NUMBER = {12},
MONTH = {1},
YEAR = {1939},
PAGES = {648--653},
DOI = {10.1073/pnas.25.12.648},
NOTE = {MR:0000643. Zbl:0023.11401. JFM:65.0874.01.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning the open subsets of a plane continuum ,”
Proc. Nat. Acad. Sci. U.S.A.
26 : 1
(January 1940 ),
pp. 24–25 .
MR
0000642
JFM
66.0970.02
Zbl
0023.11505
article
Abstract
BibTeX
@article {key0000642m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning the open subsets of a plane
continuum},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {26},
NUMBER = {1},
MONTH = {January},
YEAR = {1940},
PAGES = {24--25},
DOI = {10.1073/pnas.26.1.24},
NOTE = {MR:0000642. Zbl:0023.11505. JFM:66.0970.02.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning domains whose boundaries are compact ,”
Proc. Nat. Acad. Sci. U.S.A.
28 : 12
(December 1942 ),
pp. 555–561 .
MR
0007483
Zbl
0060.40305
article
BibTeX
@article {key0007483m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning domains whose boundaries
are compact},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {28},
NUMBER = {12},
MONTH = {December},
YEAR = {1942},
PAGES = {555--561},
DOI = {10.1073/pnas.28.12.555},
NOTE = {MR:0007483. Zbl:0060.40305.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning a continuum and its boundary ,”
Proc. Nat. Acad. Sci. U.S.A.
28 : 12
(December 1942 ),
pp. 550–555 .
MR
0007482
Zbl
0060.40304
article
Abstract
BibTeX
@article {key0007482m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning a continuum and its boundary},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {28},
NUMBER = {12},
MONTH = {December},
YEAR = {1942},
PAGES = {550--555},
DOI = {10.1073/pnas.28.12.550},
NOTE = {MR:0007482. Zbl:0060.40304.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning intersecting continua ,”
Proc. Nat. Acad. Sci. U.S.A.
28
(December 1942 ),
pp. 544–550 .
MR
0007481
Zbl
0060.40303
article
Abstract
BibTeX
@article {key0007481m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning intersecting continua},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {28},
MONTH = {December},
YEAR = {1942},
PAGES = {544--550},
DOI = {10.1073/pnas.28.12.544},
NOTE = {MR:0007481. Zbl:0060.40303.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning separability ,”
Proc. Nat. Acad. Sci. U.S.A.
28 : 2
(February 1942 ),
pp. 56–58 .
MR
0005320
Zbl
0063.04086
article
BibTeX
@article {key0005320m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning separability},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {28},
NUMBER = {2},
MONTH = {February},
YEAR = {1942},
PAGES = {56--58},
DOI = {10.1073/pnas.28.2.56},
NOTE = {MR:0005320. Zbl:0063.04086.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning continua which have dendratomic subsets ,”
Proc. Nat. Acad. Sci. U.S.A.
29 : 11
(December 1943 ),
pp. 384–389 .
MR
0009435
Zbl
0060.40306
article
BibTeX
@article {key0009435m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning continua which have dendratomic
subsets},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {29},
NUMBER = {11},
MONTH = {December},
YEAR = {1943},
PAGES = {384--389},
DOI = {10.1073/pnas.29.11.384},
NOTE = {MR:0009435. Zbl:0060.40306.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning webs in the plane ,”
Proc. Nat. Acad. Sci. U.S.A.
29 : 11
(December 1943 ),
pp. 389–393 .
MR
0009436
Zbl
0060.40307
article
BibTeX
@article {key0009436m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning webs in the plane},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {29},
NUMBER = {11},
MONTH = {December},
YEAR = {1943},
PAGES = {389--393},
DOI = {10.1073/pnas.29.11.389},
NOTE = {MR:0009436. Zbl:0060.40307.},
ISSN = {0027-8424},
}
R. L. Moore :
“Concerning tangents to continua in the plane ,”
Proc. Nat. Acad. Sci. U.S.A.
31 : 2
(February 1945 ),
pp. 67–70 .
MR
0011542
Zbl
0063.04085
article
BibTeX
@article {key0011542m,
AUTHOR = {Moore, R. L.},
TITLE = {Concerning tangents to continua in the
plane},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {31},
NUMBER = {2},
MONTH = {February},
YEAR = {1945},
PAGES = {67--70},
DOI = {10.1073/pnas.31.2.67},
NOTE = {MR:0011542. Zbl:0063.04085.},
ISSN = {0027-8424},
}
R. L. Moore :
“A characterization of a simple plane web ,”
Proc. Nat. Acad. Sci. U.S.A.
32 : 12
(December 1946 ),
pp. 311–316 .
MR
0018809
Zbl
0060.40308
article
Abstract
BibTeX
In his thesis [1946], R H Bing has shown that in order that the compact plane continuum \( M \) should be a simple web it is necessary and sufficient that it should be a continuous curve which remains connected and locally connected on the removal of any countable point set. In the present paper another characterization will be given:
Every two points of a simple plane web are separated from each other in it either by each of uncountably many mutually exclusive arcs or by each of uncountably many mutually exclusive simple closed curves.
@article {key0018809m,
AUTHOR = {Moore, R. L.},
TITLE = {A characterization of a simple plane
web},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {32},
NUMBER = {12},
MONTH = {December},
YEAR = {1946},
PAGES = {311--316},
DOI = {10.1073/pnas.32.12.311},
NOTE = {MR:0018809. Zbl:0060.40308.},
ISSN = {0027-8424},
}
R. L. Moore :
“Spirals in the plane ,”
Proc. Nat. Acad. Sci. U.S.A.
39 : 3
(March 1953 ),
pp. 207–213 .
MR
0053496
Zbl
0050.38701
article
BibTeX
@article {key0053496m,
AUTHOR = {Moore, R. L.},
TITLE = {Spirals in the plane},
JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.},
FJOURNAL = {Proceedings of the National Academy
of Sciences of the United States of
America},
VOLUME = {39},
NUMBER = {3},
MONTH = {March},
YEAR = {1953},
PAGES = {207--213},
DOI = {10.1073/pnas.39.3.207},
NOTE = {MR:0053496. Zbl:0050.38701.},
ISSN = {0027-8424},
}
R. L. Moore :
Foundations of point set theory ,
revised and enlarged edition.
AMS Colloquium Publications 13 .
American Mathematical Society (Providence, RI ),
1962 .
Republication of 1932 original .
MR
0150722
Zbl
0192.28901
book
BibTeX
@book {key0150722m,
AUTHOR = {Moore, R. L.},
TITLE = {Foundations of point set theory},
EDITION = {revised and enlarged},
SERIES = {AMS Colloquium Publications},
NUMBER = {13},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1962},
PAGES = {xi+419},
NOTE = {Republication of 1932 original. MR:0150722.
Zbl:0192.28901.},
}
F. B. Jones :
“Dedication ,”
pp. iv–x
in
Topology conference
(Emory University, Atlanta, GA, 19–21 March 1970 ).
Edited by J. W. Rogers, Jr.
Emory University (Atlanta, GA ),
1970 .
Conference dedicated to Robert Lee Moore.
MR
0342343
incollection
People
BibTeX
@incollection {key0342343m,
AUTHOR = {Jones, F. Burton},
TITLE = {Dedication},
BOOKTITLE = {Topology conference},
EDITOR = {Rogers, Jr., J. W.},
PUBLISHER = {Emory University},
ADDRESS = {Atlanta, GA},
YEAR = {1970},
PAGES = {iv--x},
NOTE = {(Emory University, Atlanta, GA, 19--21
March 1970). Conference dedicated to
Robert Lee Moore. MR:0342343.},
}
Topology conference
(Emory University, Atlanta, GA, 19–21 March 1970 ).
Edited by J. W. Rogers, Jr.
Emory University (Atlanta, GA ),
1970 .
Conference dedicated to Robert Lee Moore.
MR
0331297
Zbl
0245.00003
book
People
BibTeX
@book {key0331297m,
TITLE = {Topology conference},
EDITOR = {Rogers, Jr., J. W.},
PUBLISHER = {Emory University},
ADDRESS = {Atlanta, GA},
YEAR = {1970},
PAGES = {xiii+122},
NOTE = {(Emory University, Atlanta, GA, 19--21
March 1970). Conference dedicated to
Robert Lee Moore. MR:0331297. Zbl:0245.00003.},
}
Proceedings of the University of Oklahoma topology conference
(Norman, OK, 23–25 March 1972 ).
Edited by D. Kay, J. Green, L. Rubin, and L. P. Su .
University of Oklahoma (Norman, OK ),
1972 .
Conference dedicated to Robert Lee Moore.
MR
0341363
Zbl
0237.00017
book
People
BibTeX
@book {key0341363m,
TITLE = {Proceedings of the {U}niversity of {O}klahoma
topology conference},
EDITOR = {Kay, David and Green, John and Rubin,
Leonard and Su, Li Pi},
PUBLISHER = {University of Oklahoma},
ADDRESS = {Norman, OK},
YEAR = {1972},
PAGES = {xx+344},
NOTE = {(Norman, OK, 23--25 March 1972). Conference
dedicated to Robert Lee Moore. MR:0341363.
Zbl:0237.00017.},
}
D. R. Traylor :
“Dedication ,”
pp. i–xx
in
Proceedings of the University of Oklahoma topology conference
(Norman, OK, 23–25 March 1972 ).
Edited by D. Kay, J. Green, L. Rubin, and L. P. Su .
University of Oklahoma (Norman, OK ),
1972 .
Conference dedicated to Robert Lee Moore.
MR
0342344
incollection
People
BibTeX
@incollection {key0342344m,
AUTHOR = {Traylor, D. Reginald},
TITLE = {Dedication},
BOOKTITLE = {Proceedings of the {U}niversity of {O}klahoma
topology conference},
EDITOR = {Kay, David and Green, John and Rubin,
Leonard and Su, Li Pi},
PUBLISHER = {University of Oklahoma},
ADDRESS = {Norman, OK},
YEAR = {1972},
PAGES = {i--xx},
NOTE = {(Norman, OK, 23--25 March 1972). Conference
dedicated to Robert Lee Moore. MR:0342344.},
}
R. L. Wilder :
“Robert Lee Moore, 1882–1974 ,”
Bull. Am. Math. Soc.
82 : 3
(1976 ),
pp. 417–427 .
MR
0465747
Zbl
0329.01016
article
People
BibTeX
@article {key0465747m,
AUTHOR = {Wilder, R. L.},
TITLE = {Robert {L}ee {M}oore, 1882--1974},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {82},
NUMBER = {3},
YEAR = {1976},
PAGES = {417--427},
DOI = {10.1090/S0002-9904-1976-14029-3},
NOTE = {MR:0465747. Zbl:0329.01016.},
ISSN = {0002-9904},
}
F. B. Jones :
“The Moore method ,”
Am. Math. Monthly
84 : 4
(1977 ),
pp. 273–278 .
MR
0426988
Zbl
0351.00029
article
Abstract
People
BibTeX
While one cannot say that the “Moore Method” of teaching mathematics has gained wide-spread acceptance in college and university circles, it has been and is being successfully used by enough people to attract attention — even outside academia. Furthermore, there is considerable interest and curiosity about what it is and how it works. Mainly, for this reason, I am going to describe my own experiences in Moore’s classes and in using the method with my own students, both graduate and undergraduate.
@article {key0426988m,
AUTHOR = {Jones, F. Burton},
TITLE = {The {M}oore method},
JOURNAL = {Am. Math. Monthly},
FJOURNAL = {The American Mathematical Monthly},
VOLUME = {84},
NUMBER = {4},
YEAR = {1977},
PAGES = {273--278},
DOI = {10.2307/2318868},
NOTE = {MR:0426988. Zbl:0351.00029.},
ISSN = {0002-9890},
}
R. L. Wilder :
“The mathematical work of R. L. Moore: Its background, nature and influence ,”
Arch. Hist. Exact Sci.
26 : 1
(1982 ),
pp. 73–97 .
MR
664470
Zbl
0491.01012
article
People
BibTeX
@article {key664470m,
AUTHOR = {Wilder, R. L.},
TITLE = {The mathematical work of {R}.~{L}. {M}oore:
{I}ts background, nature and influence},
JOURNAL = {Arch. Hist. Exact Sci.},
FJOURNAL = {Archive for History of Exact Sciences},
VOLUME = {26},
NUMBER = {1},
YEAR = {1982},
PAGES = {73--97},
DOI = {10.1007/BF00348310},
NOTE = {MR:664470. Zbl:0491.01012.},
ISSN = {0003-9519},
CODEN = {AHESAN},
}
B. Fitzpatrick, Jr. :
“Some aspects of the work and influence of R. L. Moore ,”
pp. 41–61
in
Handbook of the history of general topology ,
vol. 1 .
Edited by C. E. Aull and R. Lowen .
Kluwer Academic (Dordrecht ),
1997 .
MR
1617585
Zbl
0899.54003
incollection
Abstract
People
BibTeX
There is a considerable body of literature dealing largely or in part with the life, work, teaching, influence, and legacy of R. L. Moore. This article will supply for the interested reader a list of such writings. we will comment on some of them and will elaborate on some, according to our own tastes and prejudices. The fact of their existence in the readily available literature makes it unnecessary, even if it were possible, to try to give a complete analysis of Moore’s work. We will conclude by discussing his teaching.
@incollection {key1617585m,
AUTHOR = {Fitzpatrick, Jr., Ben},
TITLE = {Some aspects of the work and influence
of {R}.~{L}. {M}oore},
BOOKTITLE = {Handbook of the history of general topology},
EDITOR = {Aull, C. E. and Lowen, R.},
VOLUME = {1},
PUBLISHER = {Kluwer Academic},
ADDRESS = {Dordrecht},
YEAR = {1997},
PAGES = {41--61},
NOTE = {MR:1617585. Zbl:0899.54003.},
ISBN = {0792344790, 9780792344797},
}
J. Parker :
R. L. Moore: Mathematician and teacher .
MAA Spectrum .
Mathematical Association of America (Washington, DC ),
2005 .
MR
2103548
Zbl
1069.01007
book
People
BibTeX
@book {key2103548m,
AUTHOR = {Parker, John},
TITLE = {R.~{L}. {M}oore: {M}athematician and
teacher},
SERIES = {MAA Spectrum},
PUBLISHER = {Mathematical Association of America},
ADDRESS = {Washington, DC},
YEAR = {2005},
PAGES = {xiv+387},
NOTE = {MR:2103548. Zbl:1069.01007.},
ISBN = {088385550X, 9780883855508},
}
L. Corry :
“A clash of mathematical titans in Austin: Harry S. Vandiver and Robert Lee Moore (1924–1974) ,”
Math. Intelligencer
29 : 4
(2007 ),
pp. 62–74 .
MR
2361623
Zbl
0554.5034
article
People
BibTeX
@article {key2361623m,
AUTHOR = {Corry, Leo},
TITLE = {A clash of mathematical titans in {A}ustin:
{H}arry~{S}. {V}andiver and {R}obert
{L}ee {M}oore (1924--1974)},
JOURNAL = {Math. Intelligencer},
FJOURNAL = {The Mathematical Intelligencer},
VOLUME = {29},
NUMBER = {4},
YEAR = {2007},
PAGES = {62--74},
DOI = {10.1007/BF02986177},
NOTE = {MR:2361623. Zbl:0554.5034.},
ISSN = {0343-6993},
CODEN = {MAINDC},
}