DECOMPOSITION OF CONTINUITY IN TERMS OF BOTH GENERALIZED TOPOLOGY AND TOPOLOGY

Abstract

Here decomposition of continuity like notion is explored in terms of generalized topology as well as topology on a set. This concept is used as a new tool to study different characterizations of a given generalized topological space, giving a new dimension in the study of topological spaces. Firstly, more properties of µ ∗ -open(closed), µ 0 -open(closed) sets, µ 0 -continuous and µ ∗ -continuous functions are studied. Also, a new family of sets µ ∗ α -open(closed) and µ 0 β -open(closed) sets are introduced. In terms of these sets, the notion of µ ∗ α -continuous and µ 0 β - continuous are defined. Interrelations, characterizations of these sets and functions are explored.