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Notes About the Carathéodory Number |
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| Authors: | Imre Bárány Roman Karasev |
| Institution: | 1. R??nyi Institute of Mathematics, Hungarian Academy of Sciences, P.O. Box 127, 1364, Budapest, Hungary 2. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, England 3. Dept. of Mathematics, Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, 141700, Russia 4. Laboratory of Discrete and Computational Geometry, Yaroslavl State University, Sovetskaya st. 14, Yaroslavl, 150000, Russia |
| Abstract: | In this paper we give sufficient conditions for a compactum in ? 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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