On pp-cluster sets and their application to pp-closedness

In this paper, the study of a new type of cluster sets for functions and multifunctions between topological spaces has been initiated by use of preopen sets of [8]. Such a notion of cluster sets is characterized and studied to some extent. In the process, a characterization of Hausdorffness is achieved in terms of the cluster set of a certain class of functions. An important application of the study is exhibited by establishing a characterization of the concept of pp-closedness of [7] via the introduced idea of cluster set of multifunctions.