On the existence of constant selections
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.
scientific article; zbMATH DE number 1462696
scientific article