Notes about the Caratheodory number

Details Notes about the Caratheodory number Notes about the Caratheodory number

2011-12-27

arxiv.org/abs/1112.5942v1

Mathematics

Metric Geometry

Scientific paper

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

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