Notes about the Caratheodory number
Metric Geometry
2012-12-27 v1 Combinatorics
Abstract
In this paper we give sufficient conditions for a compactum in to have Carath\'{e}odory number less than , 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.
Cite
@article{arxiv.1112.5942,
title = {Notes about the Caratheodory number},
author = {Imre Barany and Roman Karasev},
journal= {arXiv preprint arXiv:1112.5942},
year = {2012}
}