g-$\mathcal{H}$-regular and g-$\mathcal{H}$-normal Hereditary Spaces

Abstract

This paper presents the introduction of the concept of $g$-$\mathcal{H}$-regularity within the context of hereditary
spaces. It delves into an exploration of various properties associated with $g$-$\mathcal{H}$-normality, offering proofs
for some of these properties. Additionally, the paper investigates the characterization of $g$-$\mathcal{H}$-normality
through the application of modified versions of Urysohn's lemma and the famous Tietze Extension Theorem.