Decompositions of Continuity In Simply Extended Topological Spaces

S Nagarani

doi:10.17762/turcomat.v12i1s.1833

Abstract

In this paper, we obtain some decompositions of continuity in simply extended topological spaces.

Highlights

Semi-open, preopen sets, α-open, β-open sets or semi-preopen sets play an important role in the research of generalizations of continuity
Let us denote by σ(τ(B)) the class of all B-semiopen sets on X, by π(τ(B)) the class of all B-preopen sets on X, by α(τ(B)) the class of all B-α-open sets on X, by β(τ(B)) the class of all Bβ-open sets on X
B-semi-open, B-preopen, B-α-open, B-b-open, Bβ-open) sets is denoted by B(X)

Summary

INTRODUCTION

Semi-open, preopen sets, α-open, β-open sets or semi-preopen sets play an important role in the research of generalizations of continuity. By using these sets several authors introduced and studied various types of modifications of continuity in topological spaces. In [12] the author introduced the notions of D(m1,m2)-sets, where m1 and m2 are minimal structures on nonempty set X, and obtain useful results concerning these sets. By using these results we obtain general decompositions of M-continuity. Generalizations of the results established in [3,5,6,17,18] are

PRELIMINARIES

SIMPLE EXTENSION OF TOPOLOGIES

MINIMAL STRUCTURES

DECOMPOSITIONS OF CONTINUITY