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Analogues of the central point theorem for families with d-intersection property in ℝd

Abstract

In this paper we consider families of compact convex sets in ℝd such that any subfamily of size at most d has a nonempty intersection. We prove some analogues of the central point theorem and Tverberg’s theorem for such families.

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Correspondence to Roman N. Karasev.

Additional information

Supported by the Dynasty Foundation, the President’s of Russian Federation grant MK-113.2010.1, the Russian Foundation for Basic Research grants 10-01-00096 and 10-01-00139, the Federal Program “Scientific and scientific-pedagogical staff of innovative Russia” 2009-2013, and the Russian government project 11.G34.31.0053.

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Karasev, R.N. Analogues of the central point theorem for families with d-intersection property in ℝd . Combinatorica 32, 689–702 (2012). https://doi.org/10.1007/s00493-012-2603-5

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Mathematics Subject Classification (2000)

  • 52A20
  • 52A35
  • 52C35