Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
ISSN: 0362-546X

hal-00699030
https://hal.archives-ouvertes.fr/hal-00699030

Éditeur(s) : HAL CCSD American Mathematical Society
Résumé : International audience
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 ≤ 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 Rn 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.
ISSN: 0002-9939

hal-00699217
https://hal.archives-ouvertes.fr/hal-00699217