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

Abstract

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.

References in corpus (2)

• Dual central point theorems and their generalizations
• Tverberg-type theorems for intersecting by rays

Cited by in corpus (2)

• A tight colored Tverberg theorem for maps to manifolds
• Tverberg-type theorems for intersecting by rays