Analogues of the central point theorem for families with $d$-intersection property in $\mathbb R^d$

Details Analogues of the central point theorem for families with $d$-intersection property in $\mathbb R^d$ Analogues of the central point theorem for families with $d$-intersection property in $\mathbb R^d$

2009-06-12

arxiv.org/abs/0906.2262v1

Mathematics

Metric Geometry

Scientific paper

In this paper we consider families of compact convex sets in $\mathbb R^d$
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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