Almost β-Normality III



Definition 1: A topological space is almost normal if for every pair of disjoint closed sets E and F, one of which is regularly closed, there exist disjoint open sets U and V such that E ⊆ U and F ⊆ V. [3]

Definition 2: A topological space is β-normal if for every pair of disjoint closed sets E and F, there are open sets U and V such that E ∩ U = E, F ∩ V = F, and UV = ∅. [1]

Definition 3: A topological space is almost β-normal if for every pair of disjoint closed sets E and F, one of which is regularly closed, there are open sets U and V such that E ∩ U = E, F ∩ V = F, and UV = ∅. [2]



We will continue our discussion from last week comparing almost β-normality to other normality type properties.



[1] A. Arhangelskii, L. Ludwig, On α-normal and β-normal spaces, Comment. Math. Univ. Carolinae 42 (3) (2001) 507-519.

[2] A. Das, P. Bhat, J. Tartir, On a simultaneous generalization of β-normality and almost normality, Filomat 31 (2) (2017) 425-430.

[3] M. Singal, S. Arya, Almost normal and almost completely regular spaces, Glasnik Mat. 25 (5) (1970) 141-152.



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