Proceedings of the American Mathematical Society

Author(s): Charles D. Horvath; Marc Lassonde
Journal: Proc. Amer. Math. Soc. 125 (1997), 1209-1214.
MSC (1991): Primary 52A30, 54C99; Secondary 52A35, 52A07
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Abstract: We show that if $n$

sets in a topological space are given so that all the sets are closed or all are open, and for each $k\le n$ every $k$

of the sets have a $(k-2)$

-connected union, then the $n$

sets have a point in common. As a consequence, we obtain the following starshaped version of Helly's theorem: If every $n+1$

or fewer members of a finite family of closed sets in $\mbox {$\mathbb {R}$} ^n$ have a starshaped union, then all the members of the family have a point in common. The proof relies on a topological KKM-type intersection theorem.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 52A30, 54C99, 52A35, 52A07

Charles D. Horvath
Affiliation: Département de Mathématiques, Université de Perpignan, 66860 Perpignan Cedex, France
Email: horvath@univ-perp.fr

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