Epiregular topological spaces

Epi-α-Normality and Epi-β-Normality

“…Since every β-normal space satisfying T 1 axiom is regular (see [5]), we recall that a topological space (Y, τ) is called epiregular [8] if there is a coarser topology τ ′ on Y such that (Y, τ ′ ) is T 3 , so easily we conclude the following.…”

“…e topology on Y generated by the family of all open domain is denoted by τ s . e space (Y, τ s ) is called the semiregularization of Y [8].…”

Epi-completely Regular Topological Spaces

“…The Smirnov's deleted sequence topology is not almost-normal because the closed domain subset B = [−1, 0] is disjoint from the closed subset A = { 1 n : n ∈ N}, and they cannot be separated. Since U ⊆ T , U is the Euclidian topology on R, which is coarser than T , and (R, U) is a T 4 -space, we obtain: X is epi-normal (in fact it is sub-metrizable [5]). Since the Smirnov's deleted sequence topology is a Lindelöf non regular space, it is not L-regular [6].…”

“…The notion of epi-normality has been studied by Kalantan and Alzahrani in 2016 [15]. Then, Alzahrani studied the notion of epi-regularity in 2018 [5]. Kalantan and Alshammari studied the notion of epi-mild normality in 2018 [18].…”

“…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.…”