H*-Normal Spaces and Some Related Functions

TL;DR

This paper studies a new class of functions and spaces called H*-normal spaces, extending classical concepts and establishing their properties and relationships with other normality notions in topology.

Contribution

It introduces and characterizes H*-normal spaces and functions, generalizing existing notions and providing new theorems on their properties and preservation.

Findings

H*-normal spaces are characterized through various theorems.

Generalizations of H*-closed functions are established.

Connections between H*-normality, g-normal, and classical normal spaces are clarified.

Abstract

This paper introduces and explores functions defined on \( H^* \)-normal spaces through the framework of \( H^* \)-open sets. We extend the concept of \( H^* \)-normality and investigate its connections with \( g \)-normal and classical normal spaces. Additionally, we generalize \( H^* \)-closed and \( H^* \)-generalized closed functions, analyzing their fundamental properties. Several characterizations of \( H^* \)-normal spaces are established, along with preservation theorems that highlight the structural significance of these functions.