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arXiv · 1112.5942

Notes about the Caratheodory number

Imre Barany·Roman Karasev
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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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Imre Barany, Roman Karasev. 2011-12-27. Notes about the Caratheodory number. https://doi.org/10.1007/s00454-012-9439-z

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