Addendum to: On a simultaneous generalization of β-normality and almost normality

Das, Ananga Kumar; Bhat, Pratibha; Tartir, Jamal

doi:10.2298/fil1719021d

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Theorem 9 If Y Is Relative Almost Normal and Relative T 1 Then Y Is Relative Almost Regular1

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2021

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“…But Y is vacuously relative almost normal as there does not exist any pair of disjoint regularly closed sets in X. Definition 5 (see [16,17]). X is said to be almost β-normal if for any two disjoint closed subsets A and B of X such that A is regularly closed, there exist open subsets U and V of X such that A ∩ U is dense in A and B ∩ V is dense in B and U ∩ V � ϕ.…”

Section: Theorem 9 If Y Is Relative Almost Normal and Relative T 1 Then Y Is Relative Almost Regularmentioning

confidence: 99%

Some New Variants of Relative Regularity via Regularly Closed Sets

Raina

Das

2021

Journal of Mathematics

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Every topological property can be associated with its relative version in such a way that when smaller space coincides with larger space, then this relative property coincides with the absolute one. This notion of relative topological properties was introduced by Arhangel’skii and Ganedi in 1989. Singal and Arya introduced the concepts of almost regular spaces in 1969 and almost completely regular spaces in 1970. In this paper, we have studied various relative versions of almost regularity, complete regularity, and almost complete regularity. We investigated some of their properties and established relationships of these spaces with each other and with the existing relative properties.

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Section: Theorem 9 If Y Is Relative Almost Normal and Relative T 1 Then Y Is Relative Almost Regularmentioning

confidence: 99%