Generalized Semi-α-Closed Sets in Topology

Abstract

In 1969, Levine introduced the concept and properties of generalized closed sets (briefly g-closed), where the complement of such a set is called a generalized open set (briefly g-open). In this research, we introduce and study new classes of sets called generalized semi-α-closed sets (briefly gsα-closed) in topological spaces. We investigate and prove their relationships with other closed sets, supported by examples and counterexamples, and establish their fundamental properties such as union, intersection, and containment. We also present definitions for the closure of generalized semi-α-closed sets (briefly, gsα-cl(A)) and the interior of generalized semi-α-closed sets (briefly, gsα-int(A)), studying their key properties, providing illustrative examples, and proving their fundamental characteristics. In future studies, we aim to expand this research by introducing a new operator similar to the one currently studied in terms of topological properties.