A NEW TYPE OF CLUSTER SETS AND ITS APPLICATIONS
Keywords:delta-cluster set, multifunction, nearly compact space, nearly Lindelof space, almost regularity
In this paper we introduce the concept of a new type of cluster sets, termed $\delta$-cluster sets, of functions and multifunctions between topological spaces. Expressions of such sets are found and multifunctions with $\delta$-closed graphs are characterized. Also the behaviour of $\delta$-cluster sets toward a-continuity of a func- tion is observed. Finally as applications, we find new characterizations of almost regularity, near compactness and near Lindelofness of a topological space in terms of $\delta$-cluster sets of suitable multifunctions.
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