Epi-mild normality

Abstract

A space (X, τ) is called epi-mildly normal if there exists a coarser topology τ′ on X such that (X, τ′) is Hausdorff (T2) mildly normal. We investigate this property and present some examples to illustrate the relationships between epi-mild normality and other weaker kinds of normality.

Epi-α-Normality and Epi-β-Normality

“…Since any nontrivial Mrówka space Ψ(A) is epinormal (see [24]) and it is not α-normal (see [5]), we conclude the following.…”

New Topology on Symmetrized Omega Algebra

“…A space X is mildly normal [10] if any pair of disjoint closed domain subsets A and B of X can be separated by two disjoint open subsets. A space X, T ðÞ is epi-mildly normal [11] if there exists a coarser topology T 0 on X such that X, T 0 ðÞ is T 2 and mildly normal space. A space X, T ðÞ is epi-almost normal [12] if there exists a coarser topology T 0 on X such that X, T 0 ðÞ is T 2 and almost normal space.…”

Epi-completely Regular Topological Spaces

“…Then, Alzahrani studied the notion of epi-regularity in 2018 [5]. Kalantan and Alshammari studied the notion of epi-mild normality in 2018 [18]. At the beginning of 2020, Alshammari studied the notion of epi-almost normality [3].…”

“…A space (X, T ) is said to be epi-normal [15] (resp. epi-mildly normal [18], epi-almost normal [3], epi-regular [5], epi-quasi normal [31], epi-partially normal [32]), if there exists a topology T ′ on X coarser than T such that (X, T ′ ) is a T 4 (resp. Hausdorff mildly-normal, Hausdorff almost-normal, T 3 , Hausdorff-quasi-normal, Hausdorff partially-normal) space.…”