APPLICATIONS OF $\hat{g}^{\ast\ast}$s-CLOSED SETS IN TOPOLOGICAL SPACES

Topology is the branch of Mathematics which was introduced by Johann Benedict Listing in $19^{th}$ century and its purpose is to investigate the ideas of continuity, within the frame work of Mathematics. The authors introduces a new class of sets namely, $\hat{g}^{\ast\ast}$s-closed sets [1]. We define $\hat{g}^{\ast\ast}$s-closed sets by "A subset of a topological space $(X,\tau)$ is called a $\hat{g}^{\ast\ast}$s-closed sets if $scl (A)\subseteq U$, whenever $A \subseteq U$ and $U$ is $\hat{g}^{\ast\ast}$- open" [1]. In this paper using the concept of $\hat{g}^{\ast\ast}$s-closure, $\hat{g}^{\ast\ast}$s-interior,$\hat{g}^{\ast\ast}$s-border, $\hat{g}^{\ast\ast}$s-frontier and $\hat{g}^{\ast\ast}$s-exterior and studied some of its properties.