g*b-Homeomorphisms and Contra-g*b-continuous Maps in Topological Spaces

Abstract

In this paper, we first introduce a new class of closed maps called g*b -closed map and gb-closed map. Also, we introduce a new class of homeomorphisms called g*b -homeomorphism, gb-homeomorphism and we investigate a new generalization of contracontinuity called contra-g*b -continuity. AMSClassification (2000): 54C10,54C08,54C05.

On Contra sbĝ – Continuous functions in Topological Spaces

“…3) a gb-closed set [16] if bCl(A)  U whenever A  U and U is open in X. 4) a g*b-closed set [16] if bCl(A)  U whenever A  U and U is g-open in X. 5) a bĝ-closed set [15] if bCl(A)  U whenever A  U and U is ĝ-open in X.…”

“…In 1996, Dontchev [7] introduced and investigated a new notion of continuity called contracontinuity. Follwing this, many authors introduced various types of new generalizations of contra continuity called as contra αcontinuity, contra semi-continuity [3], contra bcontinuity [12], contra sg-continuity [5], contra gscontinuity [5], contra gb-continuity [16], contra g*bcontinuity [16], contra bĝ-continuity [15] and so on and they investigated their properties. In 2015, we introduced sbĝclosed sets [3] in Topological spaces.…”

REVIEW OF WπGR CLOSED SETS IN TOPOLOGICAL SPACES

“…Usha Parameswari and Thangavelu [8] introduced b# opensets and studied its properties in 2014. Vidhya and Parimelazhagan [9] introduced g*b closed sets in 2012. In 2014,Elvina Mary [4] introduced (gs)*-closed sets in topological spaces and studied their properties .…”

Two New Versions of the Pasting Lemma via Soft Mixed Structure

“…Especially, it has a significant place in algebraic topology. Recent years, some new forms of the pasting lemma have been introduced by many mathematicians (for example, see [15], [38]- [42] and the references therein). Motivated by the above studies, we present two new version of the pasting lemma using mixed structure on a soft topological space.…”