Notes About the Carathéodory Number

Abstract

In this paper we give sufficient conditions for a compactum in 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. © 2012 Springer Science+Business Media, LLC.