Alpha beta pi g-Normal Spaces in Topological Spaces

Hamant Kumar, Umesh Chand, Rajpal Rajbhar

Abstract: The aim of this paper is to introduce a new class of normal spaces called pi g beta-normal spaces, by using pi g beta-open sets. We prove that pi g beta-normality is a topological property and it is a hereditary property with respect to pi-open, pi g beta-closed subspaces. Further we obtain a characterization and preservation theorems for pi g beta-normal spaces. The aim of this paper is to introduce a new class of normal spaces called pi g beta-normal spaces, by using pi g beta-open sets. We prove that pi g beta-normality is a topological property and it is a hereditary property with respect to pi-open, pi g beta-closed subspaces. Further we obtain a characterization and preservation theorems for pi g beta-normal spaces.

Keywords: regular closed, pi-closed, pi g beta-closed, and pi-open sets, pre pi-closed, pi-continuous, pi g betacontinuous, piirresolute, pi g betairresolute and almost piirresolute functions, pi g beta-normal spaces