Epi-α-Normality and Epi-β-Normality

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 T 1   α -normal ( T 1   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.