A unified theory for weak separation properties

Abstract

Abstract. We devise a framework which leads to the formulation of a unified theory of normality (regularity), semi-normality (semi-regularity), s-normality (s-regularity), feeblynormality (feebly-regularity), pre-normality (pre-regularity), and others. Certain aspects of theory are given by unified proof.

A Unified Theory for Certain Weak Forms of Open Sets and Their Variant Forms

“…Hence by Proposition 2.9(a), ∩ Let ψ be an operation on a topological space (X, τ ). Then the space X is said to be a (i) ψ-T 0 space [11] if for any pair of distinct points in X there exists a ψ-open set containing one of the points but not the other. (ii) ψ-T 1 space [11] if for any two distinct points x, y of X,…”

“…A topological space (X, τ ) is said to be ψ-R 0[11,19] if for each ψ-open set U and each x ∈ U , ψ-cl({x}) ⊆ U .…”