M. E. Estill :
Concerning abstract spaces .
Ph.D. thesis ,
University of Texas at Austin ,
1949 .
Advised by R. L. Moore .
A condensed version was published in Duke Math. J. 17 :4 (1950) .
MR
2937954
phdthesis
People
BibTeX
@phdthesis {key2937954m,
AUTHOR = {Estill, Mary E.},
TITLE = {Concerning abstract spaces},
SCHOOL = {University of Texas at Austin},
YEAR = {1949},
PAGES = {58},
URL = {http://search.proquest.com/docview/301829351},
NOTE = {Advised by R. L. Moore. A
condensed version was published in \textit{Duke
Math. J.} \textbf{17}:4 (1950). MR:2937954.},
}
M. E. Estill :
“Concerning abstract spaces ,”
Duke Math. J.
17 : 4
(1950 ),
pp. 317–327 .
A condensed version of the author’s PhD thesis (1949) .
MR
42686
Zbl
0039.39303
article
BibTeX
@article {key42686m,
AUTHOR = {Estill, Mary Ellen},
TITLE = {Concerning abstract spaces},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {17},
NUMBER = {4},
YEAR = {1950},
PAGES = {317--327},
DOI = {10.1215/S0012-7094-50-01730-3},
NOTE = {A condensed version of the author's
PhD thesis (1949). MR:42686. Zbl:0039.39303.},
ISSN = {0012-7094},
}
M. E. Estill :
“Separation in non-separable spaces ,”
Duke Math. J.
18 : 3
(1951 ),
pp. 623–629 .
MR
42687
Zbl
0044.19503
article
BibTeX
@article {key42687m,
AUTHOR = {Estill, Mary Ellen},
TITLE = {Separation in non-separable spaces},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {18},
NUMBER = {3},
YEAR = {1951},
PAGES = {623--629},
DOI = {10.1215/S0012-7094-51-01854-6},
NOTE = {MR:42687. Zbl:0044.19503.},
ISSN = {0012-7094},
}
M. E. Estill :
“Concerning a problem of Souslin’s ,”
Duke Math. J.
19 : 4
(1952 ),
pp. 629–639 .
MR
50878
Zbl
0048.28401
article
Abstract
BibTeX
In the first of Fundamenta Mathematicae , Souslin [1] raised the question of the existence of a connected, linearly ordered space which is not separable and does not contain uncountably many mutually exclusive segments. Let a space have property \( X \) if and only if it is not separable and does not contain uncountably many mutually exclusive domains. It is easily shown [3] that if there exists a linearly ordered space having property \( X \) , there also exists a connected linearly ordered space having property \( X \) .
The first three parts of R. L. Moore’s Axiom 1 of [2] state that:
There exists a sequence \( G_1 \) , \( G_2 \) , \( G_3,\dots \) such that (1) for each \( n \) , \( G_n \) is a collection of regions covering \( S \) , (2) for each \( n, G_{n+1} \) is a subcollection of \( G_n \) , (3) if \( R \) is any region whatsoever, \( X \) is a point of \( R \) and \( Y \) is a point of \( R \) either identical with \( X \) or not, then there exists a natural number \( m \) such that if \( g \) is any region belonging to the collection \( G_m \) and containing \( X \) then \( \overline{g} \) is a subset of \( (R-Y)+X \) .
Call this Axiom \( 1_3 \) .
It is easily shown [4; p. 628, Theorem 12] that no linear space having property \( X \) satisfies Axiom \( 1_3 \) . It has been shown in [5] that there exists a locally connected space satisfying Axiom \( 1_3 \) and having property \( X \) , but that there does not exist a locally connected space satisfying Axiom \( 1_3 \) and having property \( X \) such that each two points can be separated by a finite point set. The theorems of this paper will prove that a necessary and sufficient condition that there exist a linear space having property \( X \) is that there exist a locally connected space satisfying Axiom \( 1_3 \) and having property \( X \) such that each two points can be separated by either a countable or a separable point set.
@article {key50878m,
AUTHOR = {Estill, Mary Ellen},
TITLE = {Concerning a problem of {S}ouslin's},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {19},
NUMBER = {4},
YEAR = {1952},
PAGES = {629--639},
DOI = {10.1215/S0012-7094-52-01967-4},
NOTE = {MR:50878. Zbl:0048.28401.},
ISSN = {0012-7094},
}
M. E. Rudin :
“Countable paracompactness and Souslin’s problem ,”
Can. J. Math.
7
(February 1955 ),
pp. 543–547 .
MR
73155
Zbl
0065.38002
article
BibTeX
@article {key73155m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {Countable paracompactness and {S}ouslin's
problem},
JOURNAL = {Can. J. Math.},
FJOURNAL = {Canadian Journal of Mathematics},
VOLUME = {7},
MONTH = {February},
YEAR = {1955},
PAGES = {543--547},
DOI = {10.4153/CJM-1955-058-8},
NOTE = {MR:73155. Zbl:0065.38002.},
ISSN = {0008-414X},
}
M. E. Rudin :
“A normal space \( X \) for which \( X\times I \) is not normal ,”
Bull. Am. Math. Soc.
77 : 2
(March 1971 ),
pp. 246 .
An expanded version of this was published in Fund. Math 73 :2 (1971–1972) .
MR
270328
Zbl
0206.51601
article
BibTeX
@article {key270328m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {A normal space \$X\$ for which \$X\times
I\$ is not normal},
JOURNAL = {Bull. Am. Math. Soc.},
FJOURNAL = {Bulletin of the American Mathematical
Society},
VOLUME = {77},
NUMBER = {2},
MONTH = {March},
YEAR = {1971},
PAGES = {246},
DOI = {10.1090/S0002-9904-1971-12702-7},
NOTE = {An expanded version of this was published
in \textit{Fund. Math} \textbf{73}:2
(1971--1972). MR:270328. Zbl:0206.51601.},
ISSN = {0002-9904},
}
M. E. Rudin :
“Partial orders on the types in \( \beta N \) ,”
Trans. Am. Math. Soc.
155 : 2
(April 1971 ),
pp. 353–362 .
MR
273581
Zbl
0212.54901
article
Abstract
BibTeX
@article {key273581m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {Partial orders on the types in \$\beta
N\$},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {155},
NUMBER = {2},
MONTH = {April},
YEAR = {1971},
PAGES = {353--362},
DOI = {10.2307/1995690},
NOTE = {MR:273581. Zbl:0212.54901.},
ISSN = {0002-9947},
}
M. E. Rudin :
“A normal space \( X \) for which \( X\times I \) is not normal ,”
Fund. Math.
73 : 2
(1971–1972 ),
pp. 179–186 .
A brief initial version was published in Bull. Am. Math. Soc. 77 :2 (1971) .
MR
293583
Zbl
0224.54019
article
BibTeX
@article {key293583m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {A normal space \$X\$ for which \$X\times
I\$ is not normal},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {73},
NUMBER = {2},
YEAR = {1971--1972},
PAGES = {179--186},
NOTE = {A brief initial version was published
in \textit{Bull. Am. Math. Soc.} \textbf{77}:2
(1971). MR:293583. Zbl:0224.54019.},
ISSN = {0016-2736},
}
M. E. Rudin :
“A normal hereditarily separable non-Lindelöf space ,”
Ill. J. Math.
16 : 4
(1972 ),
pp. 621–626 .
MR
309062
Zbl
0241.54013
article
Abstract
BibTeX
A. Hajnal and I. Juhasz have defined a Hausdorff hereditarily \( \sigma \) -separable non-\( \sigma \) -Lindelöf space. R. Countryman has raised the question of the existence of a regular, hereditarily separable, non-Lindelöf space. The purpose of this paper is to show that the existence of a Souslin tree of cardinality \( \aleph_1 \) (which is consistent with the usual axioms for set theory) implies the existence of such a space which is also normal.
@article {key309062m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {A normal hereditarily separable non-{L}indel\"of
space},
JOURNAL = {Ill. J. Math.},
FJOURNAL = {Illinois Journal of Mathematics},
VOLUME = {16},
NUMBER = {4},
YEAR = {1972},
PAGES = {621--626},
URL = {http://projecteuclid.org/euclid.ijm/1256065544},
NOTE = {MR:309062. Zbl:0241.54013.},
ISSN = {0019-2082},
}
M. E. Rudin :
“The box product of countably many compact metric spaces ,”
General Topology Appl.
2 : 4
(December 1972 ),
pp. 293–298 .
MR
324619
Zbl
0243.54015
article
Abstract
BibTeX
@article {key324619m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {The box product of countably many compact
metric spaces},
JOURNAL = {General Topology Appl.},
FJOURNAL = {General Topology and its Applications},
VOLUME = {2},
NUMBER = {4},
MONTH = {December},
YEAR = {1972},
PAGES = {293--298},
DOI = {10.1016/0016-660X(72)90022-0},
NOTE = {MR:324619. Zbl:0243.54015.},
ISSN = {0016-660X},
}
M. E. Rudin :
“Countable box products of ordinals ,”
Trans. Am. Math. Soc.
192
(1974 ),
pp. 121–128 .
MR
340022
Zbl
0289.02052
article
Abstract
BibTeX
@article {key340022m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {Countable box products of ordinals},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {192},
YEAR = {1974},
PAGES = {121--128},
DOI = {10.2307/1996824},
NOTE = {MR:340022. Zbl:0289.02052.},
ISSN = {0002-9947},
}
M. E. Rudin :
Lectures on set theoretic topology
(Laramie, WY, 12–16 August 1974 ).
CBMS Regional Conference Series in Mathematics 23 .
American Mathematical Society (Providence, RI ),
1975 .
Reprinted in 1980 .
MR
367886
Zbl
0318.54001
book
BibTeX
@book {key367886m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {Lectures on set theoretic topology},
SERIES = {CBMS Regional Conference Series in Mathematics},
NUMBER = {23},
PUBLISHER = {American Mathematical Society},
ADDRESS = {Providence, RI},
YEAR = {1975},
PAGES = {iv+76},
NOTE = {(Laramie, WY, 12--16 August 1974). Reprinted
in 1980. MR:367886. Zbl:0318.54001.},
ISSN = {0160-7642},
ISBN = {9780821816738},
}
I. Juhász, K. Kunen, and M. E. Rudin :
“Two more hereditarily separable non-Lindelöf spaces ,”
Can. J. Math.
28 : 5
(October 1976 ),
pp. 998–1005 .
MR
428245
Zbl
0336.54040
article
People
BibTeX
@article {key428245m,
AUTHOR = {Juh\'asz, I. and Kunen, K. and Rudin,
Mary Ellen},
TITLE = {Two more hereditarily separable non-{L}indel\"of
spaces},
JOURNAL = {Can. J. Math.},
FJOURNAL = {Canadian Journal of Mathematics},
VOLUME = {28},
NUMBER = {5},
MONTH = {October},
YEAR = {1976},
PAGES = {998--1005},
DOI = {10.4153/CJM-1976-098-8},
NOTE = {MR:428245. Zbl:0336.54040.},
ISSN = {0008-414X},
}
S. Shelah and M. E. Rudin :
“Unordered types of ultrafilters ,”
Topology Proc.
3 : 1
(1978 ),
pp. 199–204 .
MR
540490
Zbl
0431.03033
article
People
BibTeX
@article {key540490m,
AUTHOR = {Shelah, S. and Rudin, Mary Ellen},
TITLE = {Unordered types of ultrafilters},
JOURNAL = {Topology Proc.},
FJOURNAL = {Topology Proceedings},
VOLUME = {3},
NUMBER = {1},
YEAR = {1978},
PAGES = {199--204},
URL = {http://topology.auburn.edu/tp/reprints/v03/tp03116.pdf},
NOTE = {\textit{Proceedings of the 1978 topology
conference, {I}} (Norman, OK, 1978).
MR:540490. Zbl:0431.03033.},
ISSN = {0146-4124},
}
M. E. Rudin :
“Nikiel’s conjecture ,”
Topology Appl.
116 : 3
(December 2001 ),
pp. 305–331 .
MR
1857669
Zbl
0988.54022
article
Abstract
BibTeX
@article {key1857669m,
AUTHOR = {Rudin, Mary Ellen},
TITLE = {Nikiel's conjecture},
JOURNAL = {Topology Appl.},
FJOURNAL = {Topology and its Applications},
VOLUME = {116},
NUMBER = {3},
MONTH = {December},
YEAR = {2001},
PAGES = {305--331},
DOI = {10.1016/S0166-8641(01)00218-8},
NOTE = {MR:1857669. Zbl:0988.54022.},
ISSN = {0166-8641},
CODEN = {TIAPD9},
}