KNASTER-KURATOWSKI-MAZURKIEWICZ THEOREM IN MINIMAL GENERALIZED CONVEX SPACES

Abstract

This paper deals with some results in generalized convex spaces. The notion of minimal generalized convex space is introduced and then two well known results in nonlinear analysis, that is the open and closed versions of Fan-KKM principle in this new setting are considered. Indeed, it is shown that, for any m-closed(m-open) valued KKM map in a minimal generalized convex space, {F(z), z in D} has the finite intersection property.