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A Tverberg-type generalization of the Helly number of a convexity space |
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| Authors: | Jean-Paul Doignon John R. Reay Gerard Sierksma |
| Affiliation: | (1) Department of Econometrics, Université Libre de Bruxelles, Groningen, The Netherlands;(2) Department of Econometrics, Western Washington University, Groningen, The Netherlands;(3) Department of Econometrics, University of Groningen, Groningen, The Netherlands |
| Abstract: | In 1966 H. Tverberg gave a far reaching generalization of the well-known classical theorem of J. Radon. In this paper a similar generalization of the classical Helly theorem is given and it is shown that among these two generalized theorems a relationship holds similar to a theorem proved by F.W. Levi in 1951. Also the generalized Helly theorem in the convex product and convex sum space are investigated. |
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