On the existence of constant selections
type: Item
instance of: scholarly article
title: On the existence of constant selections
zbMATH Open document ID: 0999.54016
DOI: 10.1016/S0166-8641(99)00022-X
published in: Topology and its Applications
publication date: 2002-11-24T00:00:00Z
review text: The author of this interesting paper develops a number of results relating to the existence of a constant selection for a relation (or a multifunction) between two topological spaces. If \(\Omega:X\rightarrow Y\) is such a relation then the existence of a constant selection for \(\Omega\) is equivalent with the nonemptiness of the set \(\bigcap_{x\in X}\Omega x\). For this reason almost all the results obtained by the author give sufficient conditions for \(\Omega\) to have the finite intersection property or \(\bigcap_{x\in X}\Omega x\) be nonempty. The results obtained in the first section involve topological conditions on arbitrary intersections of cofibers (for instance such intersections be connected or homotopically trivial). The convex case of the problem is investigated in the last section in which three intersection theorems for concave-convex relations are obtained.
reviewed by: Mircea Balaj
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54C55
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 49J35
zbMATH DE Number: 1462696
zbMATH Keywords: relation
zbMATH Keywords: minimax
author: Charles D. Horvath
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1462696