A KKM-result and an application for binary and non-binary choice functions
The KKM theorem gives a sufficient condition for the intersection of a finite family of closed subsets of \(\mathbb R^n\) to be non-empty. The authors generalize this result to subsets of a class of topological spaces, called \(L\)-spaces. A generalized KKM-correspondence from a topological space \(Y\) to an \(L\)-space \(X\) is one that respects the \(L\)-structure on \(X\). Theorem 1 provides the generalization of the KKM theorem to this context. The authors then apply the result to obtain a condition on the existence of maximal elements for binary choice functions and a non-emptiness condition for non-binary choice functions.
scientific article; zbMATH DE number 1887535