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Generalizations of the theorems of Radon, Helly, and Carathéodory

✍ Scribed by V. W. Bryant; R. J. Webster


Publisher
Springer Vienna
Year
1969
Tongue
English
Weight
286 KB
Volume
73
Category
Article
ISSN
0026-9255

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📜 SIMILAR VOLUMES


A generalization of carathéodory's theor
✍ Imre Bárány 📂 Article 📅 1982 🏛 Elsevier Science 🌐 English ⚖ 812 KB

The following theorem is lproved. If the sets VI, . . . , Vn+, CR" and a E fly:: conv Vi, then there exist elements ui E Vi (i = 1, . . . , n + 1) such that a E conv{o,, . . . , un+J. Thii is a generalization of Carathtidory's theorem. By applying this and similar results some open questions are ans