Multifunctions and cluster sets

Abstract

In this article the notion of cluster set-which has been extensively studied within the framework of real and analytic function theory and to some extent for arbitrary functions between arbitrary topological spaces-is investigated for multifunctions. We generalize the notion of cluster set, extend and generalize some results for cluster sets of functions, and offer some results for multifunctions which are new for functions. In the last section, several compactness generalizations are characterized in terms of multifunctions and cluster sets.