Notes about the Caratheodory number

Abstract

In this paper we give sufficient conditions for a compactum in ${\mathbb{R}}^n$ to have Carathéodory number less than $n+1$, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carathéodory theorem and give a Tverberg type theorem for families of convex compacta.

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