Minimal \(\tau^*\)-\(g\)-Open Sets and Maximal \(\tau^*\)-\(g\)-Closed Sets in Topological Spaces

Abstract

In this paper, a new class of sets called  minimal \(\tau^*\)-\(g\)-open sets and  maximal \(\tau^*\)-\(g\)-closed sets in topological spaces are introduced. They are the subclasses of \(\tau^*\)-\(g\)-open sets and \(\tau^*\)-\(g\)-closed sets respectively. Maximal \(\tau^*\)-\(g\)-open sets and minimal \(\tau^*\)-\(g\)-closed sets in topological spaces are introduced and proved that the complement of minimal \(\tau^*\)-\(g\)-open set is maximal \(\tau^*\)-\(g\)-closed set. It is also observed that the complement of maximal \(\tau^*\)-\(g\)-open set is minimal \(\tau^*\)-\(g\)-closed set.