DECOMPOSITION OF CONTINUITY IN TERMS OF BOTH GENERALIZED TOPOLOGY AND TOPOLOGY

Pankaj Chettri; Sumiran Basnett

doi:10.56827/SEAJMMS.2022.1802.25

Pankaj Chettri Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Rangpoo - 737136, Sikkim, INDIA
Sumiran Basnett Department of Mathematics, Sikkim Manipal Institute of Technology, Sikkim Manipal University, Rangpoo - 737136, Sikkim, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2022.1802.25

Keywords: : µ 0 -continuous, µ ∗ -continuous functions, µ ∗ α -open, µ 0 β - open set, µ ∗ α -continuous, µ 0 β -continuous functions

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.