Geodesic
A Proof of Bárány's Theorem
Publications de l'Institut Mathématique, _N_S_55 (1994) no. 69, p. 47 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 : 52A35 
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     author = {\v{Z}ana Kovijani\'c},
     title = {A {Proof} of {B\'ar\'any's} {Theorem}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {47 },
     publisher = {mathdoc},
     volume = {_N_S_55},
     number = {69},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a6/}
}
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Žana Kovijanić. A Proof of Bárány's Theorem. Publications de l'Institut Mathématique, _N_S_55 (1994) no. 69, p. 47 . http://geodesic.mathdoc.fr/item/PIM_1994_N_S_55_69_a6/