K. Kuperberg and W. Kuperberg :
“On weakly zero-dimensional mappings ,”
Colloq. Math.
22 : 2
(1971 ),
pp. 245–248 .
MR
281172 Zbl
0215.23904 article
People
BibTeX
@article {key281172m,
AUTHOR = {Kuperberg, K. and Kuperberg, W.},
TITLE = {On weakly zero-dimensional mappings},
JOURNAL = {Colloq. Math.},
FJOURNAL = {Colloquium Mathematicum},
VOLUME = {22},
NUMBER = {2},
YEAR = {1971},
PAGES = {245--248},
NOTE = {MR:281172. Zbl:0215.23904.},
ISSN = {0010-1354},
}
K. Kuperberg and W. Kuperberg :
“An example concerning the cancellability of cycles Topology Proc.
4 : 1
(1979 ),
pp. 133–137 .
Edited by Ross Geoghegan.
MR
583696 Zbl
0447.55009 article
Abstract
People
BibTeX
The notion of cancellability of cycles was used in [Borsuk 1976] to establish some facts about simplicity of certain shapes. The aim of this note is to solve the following problem posed in [Borsuk 1976]: Let \( A \) be a subset of \( H_n(X,G) \) and \( k \neq n \) . Is the set of cycles \( a \in H_k(X,G) \) cancellable rel. \( A \) always a subgroup of \( H_k(X,G) \) ? We construct an example solving this problem in the negative.
@article {key583696m,
AUTHOR = {Kuperberg, K. and Kuperberg, W.},
TITLE = {An example concerning the cancellability
of cycles},
JOURNAL = {Topology Proc.},
FJOURNAL = {Topology Proceedings},
VOLUME = {4},
NUMBER = {1},
YEAR = {1979},
PAGES = {133--137},
URL = {http://topology.nipissingu.ca/tp/reprints/v04/tp04113s.pdf},
NOTE = {Edited by Ross Geoghegan. MR:583696.
Zbl:0447.55009.},
ISSN = {0146-4124},
}
K. Kuperberg, W. Kuperberg, and W. R. R. Transue :
“On the 2-homogeneity of Cartesian products Fund. Math.
110 : 2
(1980 ),
pp. 131–134 .
Dedicated to the memory and Ralph Bennett.
MR
600586 Zbl
0475.54025 article
Abstract
People
BibTeX
@article {key600586m,
AUTHOR = {Kuperberg, K. and Kuperberg, W. and
Transue, W. R. R.},
TITLE = {On the 2-homogeneity of {C}artesian
products},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae. Polska Akademia
Nauk},
VOLUME = {110},
NUMBER = {2},
YEAR = {1980},
PAGES = {131--134},
DOI = {10.4064/fm-110-2-131-134},
URL = {http://matwbn.icm.edu.pl/ksiazki/fm/fm110/fm110112.pdf},
NOTE = {Dedicated to the memory and Ralph Bennett.
MR:600586. Zbl:0475.54025.},
ISSN = {0016-2736},
}
K. M. Kuperberg, W. Kuperberg, P. Minc, and C. S. Reed :
“Examples related to Ulam’s fixed point problem Topol. Methods Nonlinear Anal.
1 : 1
(1993 ),
pp. 173–181 .
MR
1215264 Zbl
0787.54041 article
People
BibTeX
@article {key1215264m,
AUTHOR = {Kuperberg, Krystyna M. and Kuperberg,
W\l odzimierz and Minc, Piotr and Reed,
Coke S.},
TITLE = {Examples related to {U}lam's fixed point
problem},
JOURNAL = {Topol. Methods Nonlinear Anal.},
FJOURNAL = {Topological Methods in Nonlinear Analysis},
VOLUME = {1},
NUMBER = {1},
YEAR = {1993},
PAGES = {173--181},
DOI = {10.12775/TMNA.1993.013},
URL = {https://projecteuclid.org/euclid.tmna/1479287198},
NOTE = {MR:1215264. Zbl:0787.54041.},
ISSN = {1230-3429},
}
K. Kuperberg and W. Kuperberg :
“Translates of a starlike plane region with a common point ,”
pp. 205–216
in
Intuitive geometry
(Szeged, Hungary, 2–7 September 1991) ).
Edited by K. Böröczky and G. Fejes Tóth .
Colloquia Mathematica Societatis Janos Bolyai 63 .
North-Holland (Amsterdam ),
1994 .
MR
1383627 Zbl
0823.52005 incollection
People
BibTeX
@incollection {key1383627m,
AUTHOR = {Kuperberg, K. and Kuperberg, W.},
TITLE = {Translates of a starlike plane region
with a common point},
BOOKTITLE = {Intuitive geometry},
EDITOR = {B\"or\"oczky, K. and Fejes T\'oth, G.},
SERIES = {Colloquia Mathematica Societatis Janos
Bolyai},
NUMBER = {63},
PUBLISHER = {North-Holland},
ADDRESS = {Amsterdam},
YEAR = {1994},
PAGES = {205--216},
NOTE = {(Szeged, Hungary, 2--7 September 1991)).
MR:1383627. Zbl:0823.52005.},
ISSN = {0139-3383},
ISBN = {9780444819062},
}
K. M. Kuperberg, W. Kuperberg, and W. R. R. Transue :
“Homology separation and 2-homogeneity ,”
pp. 287–295
in
Continua
(Cincinnati, OH, 12–15 January 1994 ).
Edited by H. Cook, W. T. Ingram, K. T. Kuperberg, A. Lelek, and P. Minc .
Lecture Notes in Pure and Applied Mathematics 170 .
Dekker (New York ),
1995 .
MR
1326851 Zbl
0826.54026 incollection
Abstract
People
BibTeX
The homology separation axiom is introduced to investigate homogeneity properties of Cartesian products of continua. We prove that under certain conditions of a homological nature the products are factorwise rigid. Also, if the product \( X\times Y \) of an \( n \) -dimensional representable continuum \( X \) and a non-degenerate continuum \( Y \) is 2-homogeneous, then \( X \) is locally \( n \) -acyclic. In particular, the product \( B\times Y \) of a \( \mu^n \) -manifold \( B \) (based on the \( n \) -dimensional Menger universal compactum \( \mu^n \) ) with any non-degenerate continuum \( Y \) is not 2-homogeneous. These theorems generalize a previous result of the same authors and some results of J. Kennedy Phelps.
@incollection {key1326851m,
AUTHOR = {Kuperberg, Krystyna M. and Kuperberg,
W\l odzimierz and Transue, William R.
R.},
TITLE = {Homology separation and 2-homogeneity},
BOOKTITLE = {Continua},
EDITOR = {Cook, Howard and Ingram, W. T. and Kuperberg,
K. T. and Lelek, Andrew and Minc, Piotr},
SERIES = {Lecture Notes in Pure and Applied Mathematics},
NUMBER = {170},
PUBLISHER = {Dekker},
ADDRESS = {New York},
YEAR = {1995},
PAGES = {287--295},
NOTE = {(Cincinnati, OH, 12--15 January 1994).
MR:1326851. Zbl:0826.54026.},
ISSN = {0075-8469},
ISBN = {9780824796501},
}
A. Bezdek, K. Kuperberg, and W. Kuperberg :
“Mutually contiguous translates of a plane disk Duke Math. J.
78 : 1
(April 1995 ),
pp. 19–31 .
MR
1328750 Zbl
0829.52008 article
People
BibTeX
@article {key1328750m,
AUTHOR = {Bezdek, A. and Kuperberg, K. and Kuperberg,
W.},
TITLE = {Mutually contiguous translates of a
plane disk},
JOURNAL = {Duke Math. J.},
FJOURNAL = {Duke Mathematical Journal},
VOLUME = {78},
NUMBER = {1},
MONTH = {April},
YEAR = {1995},
PAGES = {19--31},
DOI = {10.1215/S0012-7094-95-07802-8},
NOTE = {MR:1328750. Zbl:0829.52008.},
ISSN = {0012-7094},
}
K. Kuperberg, W. Kuperberg, J. Matoušek, and P. Valtr :
“Almost-tiling the plane by ellipses Discrete Comput. Geom.
22 : 3
(1999 ),
pp. 367–375 .
MR
1706602 Zbl
0952.52016 ArXiv
math/9804040 article
Abstract
People
BibTeX
For any \( \lambda > 1 \) we construct a periodic and locally finite packing of the plane with ellipses whose \( \lambda \) -enlargement covers the whole plane. This answers a question of Imre Bárány. On the other hand, we show that if \( \mathcal{C} \) is a packing in the plane with circular disks of radius at most 1, then its \( (1+10^{-5} \) )-enlargement covers no square with side length 4.
@article {key1706602m,
AUTHOR = {Kuperberg, K. and Kuperberg, W. and
Matou\v{s}ek, J. and Valtr, P.},
TITLE = {Almost-tiling the plane by ellipses},
JOURNAL = {Discrete Comput. Geom.},
FJOURNAL = {Discrete \& Computational Geometry},
VOLUME = {22},
NUMBER = {3},
YEAR = {1999},
PAGES = {367--375},
DOI = {10.1007/PL00009466},
NOTE = {ArXiv:math/9804040. MR:1706602. Zbl:0952.52016.},
ISSN = {0179-5376},
}
I. Bárány, K. Kuperberg, and T. Zamfirescu :
“Total curvature and spiralling shortest paths 167–176
in
U.S.-Hungarian workshops on discrete geometry and convexity
(Budapest, 12–16 July 1999 and Auburn, AL, 21–26 March 2000 ),
published as Discrete Comput. Geom.
30 : 2 .
Issue edited by G. Fejes Tóth and W. Kuperberg .
Springer (New York ),
August 2003 .
MR
2007957 Zbl
1043.52004 ArXiv
math/0301338 incollection
Abstract
People
BibTeX
This paper gives a partial confirmation of a conjecture of Agarwal, Har-Peled, Sharir, and Varadarajan that the total curvature of a shortest path on the boundary of a convex polyhedron in \( \mathbb{R}^3 \) cannot be arbitrarily large. It is shown here that the conjecture holds for a class of polytopes for which the ratio of the radii of the circumscribed and inscribed ball is bounded. On the other hand, an example is constructed to show that the total curvature of a shortest path on the boundary of a convex polyhedron in \( \mathbb{R}^3 \) can exceed \( 2\pi \) . Another example shows that the spiralling number of a shortest path on the boundary of a convex polyhedron can be arbitrarily large.
@article {key2007957m,
AUTHOR = {B\'ar\'any, Imre and Kuperberg, Krystyna
and Zamfirescu, Tudor},
TITLE = {Total curvature and spiralling shortest
paths},
JOURNAL = {Discrete Comput. Geom.},
FJOURNAL = {Discrete \& Computational Geometry},
VOLUME = {30},
NUMBER = {2},
MONTH = {August},
YEAR = {2003},
PAGES = {167--176},
DOI = {10.1007/s00454-003-0001-z},
NOTE = {\textit{U.{S}.-{H}ungarian workshops
on discrete geometry and convexity}
(Budapest, 12--16 July 1999 and Auburn,
AL, 21--26 March 2000). Issue edited
by G. Fejes T\’oth and W. odimierz Kuperberg.
ArXiv:math/0301338. MR:2007957. Zbl:1043.52004.},
ISSN = {0179-5376},
}
G. Kuperberg, K. Kuperberg, and W. Kuperberg :
“Lattice packings with gap defects are not completely saturated ,”
Beitr. Algebra Geom.
45 : 1
(2004 ),
pp. 267–273 .
MR
2070648 Zbl
1054.52010 ArXiv
math/0303366 article
Abstract
People
BibTeX
We show that a honeycomb circle packing in \( \mathbb{R}^2 \) with a linear gap defect cannot be completely saturated, no matter how narrow the gap is. The result is motivated by an open problem of G. Fejes Tóth, G. Kuperberg, and W. Kuperberg, which asks whether a honeycomb circle packing with a linear shift defect is completely saturated. We also show that an fcc sphere packing in \( \mathbb{R}^3 \) with a planar gap defect is also not completely saturated.
@article {key2070648m,
AUTHOR = {Kuperberg, Greg and Kuperberg, Krystyna
and Kuperberg, W\l odzimierz},
TITLE = {Lattice packings with gap defects are
not completely saturated},
JOURNAL = {Beitr. Algebra Geom.},
FJOURNAL = {Beitr\"age zur Algebra und Geometrie},
VOLUME = {45},
NUMBER = {1},
YEAR = {2004},
PAGES = {267--273},
NOTE = {ArXiv:math/0303366. MR:2070648. Zbl:1054.52010.},
ISSN = {0138-4821},
}
