Meekly SC*-Normal Spaces in Topological Spaces

TL;DR

This paper introduces meekly $SC^*$-normality, a new generalization of normality in topology, unifying various separation axioms and expanding the theoretical framework of generalized normal spaces.

Contribution

It develops the concept of meekly $SC^*$-normality, providing fundamental properties, characterizations, and relationships with existing normality concepts in topology.

Findings

Established properties and characterizations of meekly $SC^*$-normal spaces

Connected meekly $SC^*$-normality with existing normality concepts

Opened new research directions in generalized topological separation axioms

Abstract

This chapter develops the concept of \textbf{meekly $SC^*$-normality}, a novel generalization of the classical notion of normality in topology. The proposed framework simultaneously broadens $SC^*$-normality and other established forms of normality, offering a unified perspective on generalized separation axioms. Fundamental properties are systematically derived, several equivalent characterizations are obtained, and the relationships between meekly $SC^*$-normal spaces and a range of existing normal-type spaces are rigorously analyzed. By establishing these structural connections, the chapter not only enriches the theory of generalized closed sets and separation axioms but also opens new directions for further research in advanced topological studies.