Notes About the Carathéodory Number

@article{Brny2012NotesAT,
  title={Notes About the Carath{\'e}odory Number},
  author={I. B{\'a}r{\'a}ny and R. Karasev},
  journal={Discrete \& Computational Geometry},
  year={2012},
  volume={48},
  pages={783-792}
}
In this paper we give sufficient conditions for a compactum in ℝn 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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