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A Tverberg-type generalization of the Helly number of a convexity space

par Doignon, Jean-Paul ;Reay, John J.R.;Sierksma, Gerard
Référence Journal of geometry, 16, 1, page (117-125)
Publication Publié, 1981-12

Article révisé par les pairs

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Résumé :

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. © 1981 Birkhäuser Verlag.