PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 55(69), pp. 4750 (1994) 

A proof of Bárány's theoremZana Kovijani\'cPripodnomatematicki fakultet, Podgorica, YugoslaviaAbstract: We give a new proof of the following theorem of I. Bárány and L. Lowasz: Let $\Cal S_1,\Cal S_2,\dots,\Cal S_{d+1}$ be finite nonempty families of convex sets from $R^d$ and suppose that for any choice $C_1\in\Cal S_1,\dots,C_{d+1}\in\Cal S_{d+1}$ the intersection $C_i$ is not empty. Then for some $i=1,\dots,d+1$ all the sets in family $S_i$ have a common point. Classification (MSC2000): 52A35 Full text of the article:
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