Softly $\pi g\hat{D}$-Normal Spaces

Abstract

The aim of this paper is to introduce a new class of softly normal called softly $\pi g\widehat{D}$ -normality by using $\pi g\widehat{D}$ -open sets and obtained several properties of such a space. We discuss many properties of this new space and we give some properties that connect this new spaces with some other topological spaces, also we present some examples and counter examples that show the relationships between softly $\pi g\widehat{D}$ -normal spaces and some other topological spaces, also we introduced the concept of $\pi g\widehat{D}$ -normal, almost $\pi g\widehat{D}$ -normal, quasi $\pi g\widehat{D}$ -normal, mildly $\pi g\widehat{D}$ -normal. The main result of this paper is that softly $\pi g\widehat{D}$ -normality is a topological property and it is a hereditary property with respect to closed domain subspaces. Moreover, we obtain some new characterizations and preservation theorems of softly $\pi g\widehat{D}$ -normal spaces. We insure that existence of utility for new results of softly $\pi g\widehat{D}$ -normality using separation axioms in topological spaces which is separate on a known separation axioms in topological spaces.