SC*-Normal spaces and some functions

TL;DR

The paper introduces SC^*-normal spaces, defined via SC^*-open/closed sets, and situates them among classical normality notions. It develops a broad framework of generalized SC^*-closed and SC^*-open-type functions, including strongly, almost irresolute, and quasi-closed maps, and establishes characterizations and preservation theorems linking these mappings to SC^*-normality. Through a suite of equivalences and composition results, the authors demonstrate how various map classes preserve or reflect $SC^*$-normality and related closure properties. The work advances understanding of how generalized closure concepts interact with separation axioms, offering concrete criteria and examples to guide further study in topological normality under nonstandard closure operations. These findings have potential implications for constructing and analyzing spaces where classical normality is weakened but still retains robust separation via SC^*$-type structures.

Abstract

In this paper, we introduce and explore a new class of topological spaces termed as SC*-normal spaces, defined via SC*-open sets. The concept of SC*-normality is analyzed in relation to classical notions such as normal spaces and g-normal spaces. We further define and examine generalized forms of SC*-closed functions, including SC*-generalized closed mappings, and investigate their fundamental properties. Several characterizations of SC*-normal spaces are established, and various preservation theorems under different types of functions are also presented.