H*-Normal Spaces and Some Related Functions

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