SC*-Regular spaces and some functions

TL;DR

This paper introduces SC*-regular spaces, a new class of topological spaces, and explores their properties, relationships with existing concepts, and associated functions, advancing the understanding of generalized regularity in topology.

Contribution

It defines SC*-regular spaces, investigates their properties, and establishes connections with various regularity concepts, offering new characterizations and insights in topological regularity theory.

Findings

Defined SC*-regular spaces and their properties

Established relationships with existing regularity concepts

Presented characterizations and preservation theorems for SC*-regular spaces

Abstract

This paper introduces a novel class of topological spaces, termed SC*-regular spaces, which are defined using SC*-open sets. We explore their fundamental properties and examine their connections with existing regularity concepts, such as regular, almost, softly, weakly, alpha, zeta, and generalized-regular spaces respectively. Furthermore, we examined and define, analyze generalized SC*-closed sets and SC*-generalized closed functions, establishing key properties and preservation theorems. Several characterizations of SC*-regular spaces are also presented, providing new insights into generalized regularity in topology.