Introducing P ̂-Open Sets and Related Topological Operators

Abstract

         This paper introduces a new class of open sets, referred to as -open sets, within the framework of general topology. It is shown that the family of all -open sets generates a topology that lies precisely between the classes of -open sets and ordinary open sets. Based on this concept, several associated topological operators are defined and investigated, namely the -interior, the -closure, and the -derived set. The study highlights the fundamental properties of these operators, the interrelationships among them, and their significance in extending the theory of generalized open sets and the corresponding topological structures.