Weak normality properties and factorizations of normality

Abstract

Variants of δ-normality and δ-normal separation called weakly (functionally) δ-normal spaces are introduced and studied. This yields new factorizations of normality and δ-normality. A Urysohn type lemma and a Tietze type extension theorem for (weakly) functionally δ-normal spaces are obtained.

∆-normal spaces and decompositions of normality

“…However, none of the above implications is reversible as is well exhibited by the following examples and Example 3.8 in [8]. Proof.…”

“…Another decomposition of normality was given in [6] in terms of θ-normality and its variants. Mack [10] introduced δ-normal spaces and the same has been utilised in [8] to give a factorization of normality. In an attempt to get another decomposition of normality in terms of seminormal spaces, in this paper we introduce the notion of ∆-normal spaces.…”

A uniform approach to normality for topological spaces

“…Therefore (λ, µ)-normality just becomes normality. (ii) λ = int τ1 and µ = int τ2 , two different interior operators over two different topologies τ 1 and τ 2 , then (λ, µ)-normality becomes pairwise normality [9] of (X, τ 1 , τ 2 ) (iii) λ =interior operator and µ = cl * θ operator, then (λ, µ)-normality becomes θ-normality [8]. This is due to fact that cl θ ∈ Γ, that is, cl θ operator is monotonic.…”

A decomposition of normality via a generalization of $\kappa$-normality

“…exist in the literature. Recently, Interrelation among some of these variants of normality was studied in [4] and factorizations of normality are obtained in [4,5,12,14]. In this paper, we tried to exhibit the interrelations that exist among these generalized notions of normality and introduced a simultaneous generalization of κ-normality and weak θ-normality called weak κ-normality.…”