Abstract:
Several results on the topology of the space of kk-flats in Rn similar to the Borsuk-Ulam theorem on coverings of a sphere and a ball are proved. Some corollaries on common transversals for families of subsets of Rn and on measure partitions by hyperplanes are deduced.
Bibliography: 22 titles.
Keywords:
Borsuk-Ulam theorem, common transversals, Helly-type theorems.
Citation:
R. N. Karasev, “Theorems of Borsuk-Ulam type for flats and common transversals of families of convex compact sets”, Sb. Math., 200:10 (2009), 1453–1471
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\paper Theorems of Borsuk-Ulam type for flats and common transversals of families of convex compact sets
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\yr 2009
\vol 200
\issue 10
\pages 1453--1471
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Linking options:
https://www.mathnet.ru/eng/sm6376
https://doi.org/10.1070/SM2009v200n10ABEH004045
https://www.mathnet.ru/eng/sm/v200/i10/p39
This publication is cited in the following 6 articles:
Oleg R. Musin, “Generalizations of Tucker–Fan–Shashkin Lemmas”, Arnold Math J., 2:3 (2016), 299
B. Matschke, “A parametrized version of the Borsuk-Ulam-Bourgin-Yang-Volovikov theorem”, J. Topol. Anal., 6:2 (2014), 263–280
A. Akopyan, R. Karasev, “Cutting the same fraction of several measures”, Discrete Comput. Geom., 49:2 (2013), 402–410
Montejano L., Karasev R.N., “Topological transversals to a family of convex sets”, Discrete Comput. Geom., 46:2 (2011), 283–300
Karasev R.N., “Tverberg-Type Theorems for Intersecting by Rays”, Discrete Comput. Geom., 45:2 (2011), 340–347
R. N. Karasev, “Topological methods in combinatorial geometry”, Russian Math. Surveys, 63:6 (2008), 1031–1078
Citation in format AMSBIB
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