On $\pi g^\ast$s-Irresolute Functions in Topological Spaces

Abstract

The purpose of this paper is to defined and studied the notion of $\pi$ generalized star semi-closed sets in topological spaces and some of their basic properties are investigated. This new class of sets lies between the class of $\pi$g-closed sets and the class of $\pi$gs-closed sets. Further the notion of $\pi g^\ast$s-open sets, $\pi g^\ast$s-continuous functions and $\pi g^\ast$s-irresolute functions are defined and the composition of two $\pi g^\ast$s-irresolute functions are discussed. Several examples are provided to illustrate the behaviour of new sets and functions.