Epi-α-Normality and Epi-β-Normality

Abstract

A topological space Y,τ is called epi-α-normal (epi-β-normal) if there is a coarser topology τ′ on Y such that Y,τ′ is T1 α-normal (T1 β-normal). We investigate these properties and show some examples to explain the relationships of epi-α-normal (epi-β-normal) with other weaker versions of normality and some topological spaces.