On DS*-sets and decompositions of continuous functions

Abstract

In this paper, the notions of DS * -sets and DS * -continuous functions are introduced and their properties and their relationships with some other types of sets are investigated. Moreover, some new decompositions of continuous functions are obtained by using DS * -continuous functions, DS-continuous functions and D-continuous functions.

On Zα-Open Sets and Decompositions of Continuity

“…Tong [21] introduced the notion of B-set and B-continuity in topological spaces. The concept of A * -sets, DS -set, A * -continuity, DS-continuity introduced by E. Ekici [4,8] and used them to obtain a new decomposition of continuity. Noiri et.al [17] introduced the notion of η-set and η-continuity in topological spaces.…”