## Almost β-Normality II

**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
U
∩
V
=
∅.
[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
U
∩
V
=
∅.
[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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