On \(\alpha\)-Generalized Star Closed Sets in Bitopological Spaces

Abstract

S. Somasundaram,  M. Murugalingam and S. Palaniammal [1] introduced the concepts of \(\alpha\)-generalized star closed sets and \(\alpha\)-generalized star open sets in a topological space.  A subset \(A\) of a topological space \(X\) is called \(\alpha\)-generalized star (briefly, \(\alpha g^*\)-closed set)  if \(cl(A)\subseteq U\) whenever \(A\subseteq U\) and \(U\) is \(\alpha\)-open in \(X\). The complement of \(\alpha g^*\)-open set if \(X−A\) is \(\alpha g^*\)-closed.  In this paper, the same concept was extended to bitopological spaces and we introduced the newly related concept of pairwise αg∗αg∗-continuous mappings. Also \(alpha G^∗O \)-connectedness and \(\alpha G^∗O \)-compactness are introduced in bitopological spaces and some of their properties are established.