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Sbornik: Mathematics, 2009, Volume 200, Issue 10, Pages 1453–1471
DOI: https://doi.org/10.1070/SM2009v200n10ABEH004045 (Mi sm6376) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Theorems of Borsuk-Ulam type for flats and common transversals of families of convex compact sets

R. N. Karasev

Moscow Institute of Physics and Technology
English version PDF (339 kB) Citations (6)
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DOI: https://doi.org/10.1070/SM2009v200n10ABEH004045
Abstract: Several results on the topology of the space of $k$-flats in $\mathbb R^n$ 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 $\mathbb R^n$ and on measure partitions by hyperplanes are deduced.
Bibliography: 22 titles.
Keywords: Borsuk-Ulam theorem, common transversals, Helly-type theorems.
Received: 05.06.2008 and 30.06.2009
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 10, Pages 39–58
DOI: https://doi.org/10.4213/sm6376
Bibliographic databases:
UDC: 514.17+514.172
MSC: 52A35, 55M30, 55M35
Language: English
Original paper language: Russian
Citation: R. N. Karasev, “Theorems of Borsuk-Ulam type for flats and common transversals of families of convex compact sets”, Mat. Sb., 200:10 (2009), 39–58; Sb. Math., 200:10 (2009), 1453–1471
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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