Epi-\(\alpha\)-normality and epi-\(\beta\)-normality (Q2666172)

Summary: A topological space \((Y, \tau)\) is called epi-\(\alpha\)-normal (epi-\(\beta\)-normal) if there is a coarser topology \(\tau^\prime\) on \(Y\) such that \((Y, \tau^\prime)\) 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.