Epi- α -Normality and Epi- β -Normality

Abstract

A topological space $\left(Y,\tau \right)$ is called epi- $\alpha$ -normal (epi- $\beta$ -normal) if there is a coarser topology ${\tau }^{\prime }$ on $Y$ such that $\left(Y,{\tau }^{\prime }\right)$ is $T_1\alpha$ -normal ( $T_1\beta$ -normal). We investigate these properties and show some examples to explain the relationships of epi- $\alpha$ -normal (epi- $\beta$ -normal) with other weaker versions of normality and some topological spaces.