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
@article{PIM_1994_N_S_55_69_a6,
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/}
}
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/