On $a$-locally closed sets

TL;DR

This paper introduces the concept of $a$-locally closed sets using $a$-open sets, explores their properties, characterizations, and relationships with other local closed set types, expanding the theoretical framework in topology.

Contribution

It defines and studies the properties of $a$-locally closed sets, a new concept in topology, and relates it to existing local closed set notions.

Findings

Characterization of $a$-locally closed sets

Properties and fundamental results established

Relationships with other local closed sets clarified

Abstract

The aim of this paper is to introduce the notion of $a$-locally closed set by utilizing $a$-open sets defined by Ekici and to study some properties of this new notion. Also, some characterizations and many fundamental results regarding this new concept are obtained. Moreover, the relationships between the concepts defined within the scope of this study and some other types of local closed sets in the literature have been revealed.