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Mat. Sb., 2009, Volume 200, Number 10, Pages 39–58 (Mi msb6376)  

This article is cited in 5 scientific papers (total in 5 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

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.

DOI: https://doi.org/10.4213/sm6376

Full text: PDF file (555 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:10, 1453–1471

Bibliographic databases:

UDC: 514.17+514.172
MSC: 52A35, 55M30, 55M35
Received: 05.06.2008 and 30.06.2009

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R. N. Karasev, “Topological methods in combinatorial geometry”, Russian Math. Surveys, 63:6 (2008), 1031–1078  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Montejano L., Karasev R.N., “Topological transversals to a family of convex sets”, Discrete Comput. Geom., 46:2 (2011), 283–300  crossref  mathscinet  zmath  isi  elib  scopus
    3. Karasev R.N., “Tverberg-Type Theorems for Intersecting by Rays”, Discrete Comput. Geom., 45:2 (2011), 340–347  crossref  mathscinet  zmath  isi  elib  scopus
    4. A. Akopyan, R. Karasev, “Cutting the same fraction of several measures”, Discrete Comput. Geom., 49:2 (2013), 402–410  crossref  mathscinet  zmath  isi  elib  scopus
    5. B. Matschke, “A parametrized version of the Borsuk-Ulam-Bourgin-Yang-Volovikov theorem”, J. Topol. Anal., 6:2 (2014), 263–280  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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