KKM type theorems with boundary conditions

TL;DR

This paper generalizes classical KKM theorems by relaxing boundary conditions and broadening the types of spaces and covers involved, thus extending their applicability in mathematical and economic theories.

Contribution

It introduces weaker boundary assumptions and more general spaces and covers in KKM-type theorems, expanding their theoretical scope.

Findings

Broader class of spaces and covers considered

Weaker boundary conditions established

Generalizations extend applicability of KKM theorems

Abstract

We consider generalizations of Gale's colored KKM lemma and Shapley's KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions.