On a Simultaneous Generalization of β-Normality and Almost Normality

Abstract

A new generalization of normality called almost $\beta$-normality is introduced and studied which is a simultaneous generalization of almost normality and $\beta$-normality. A topological space is called almost $\beta$-normal if for every pair of disjoint closed sets $A$ and $B$ one of which is regularly closed (Say $A$), there exist disjoint open sets $U$ and $V$ such that $\overline{U \cap V }= A $ , $\overline{U \cap V}= B$ and $\overline{U} \cap \overline{V} = \phi$.