SC*-Normal spaces and some functions

TL;DR

This paper introduces SC*-normal spaces, a new class of topological spaces, and studies their properties, relationships with existing spaces, and the behavior of generalized closed functions within this framework.

Contribution

It defines SC*-normal spaces, explores their properties, and establishes new theorems on their characterization and preservation under various functions.

Findings

SC*-normal spaces are characterized and related to classical normal spaces.

Preservation theorems for SC*-normal spaces under different functions are established.

Generalized SC*-closed functions are analyzed with their fundamental properties.

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.