On gr*-Closed Sets in a Topological Spaces

Abstract

The aim of this paper is to introduce the concept of generalized regular star closed sets and study some of its properties.

On (gg)*- Closed Sets in Topological Spaces

“…(32) generalized regular star closed (briefly gr *-closed) [31] if rcl (A)  U whenever A  U and U is g -open in X.…”

On ψg* - Closed Sets in Topological Spaces

“…4) a αg-closed set [10] if αCl(A)  U whenever A  U and U is open in X. 5) a gr*-closed set [7] if rCl(A)  U whenever A  U and U is g-open in X. 6) a g*-closed set [16] if Cl(A)  U whenever A  U and U is g-open in X.…”

A study on gr*-closed sets in Bitopological Spaces

“…In 1985, Fukutake [2] introduced the concept of g-closed sets in bitopological spaces and after that several authors turned their attention towards generalizations of various concepts of topology by considering bitopological spaces and Indirani et.al. [5] introduced gr*-closed sets in topological spaces and investigated its relationship with the other types of closed sets. The purpose of the present paper is to define a new class of closed sets called (i,j) gr*-closed sets and we discuss some basic properties of (i,j) gr*-closed sets in bitopological spaces.…”

“…Definition 2.5 A map f:(X, τ 1, τ 2 )→( (Y, τ 1, τ 2 ) is called: [4] and D r * (i,j)-σ k -continuous [6]) if the inverse image of every σ k -closed set is (i,j)-g-closed (resp. (i,j)-g…”