Soft Slight Omega-Continuity and Soft Ultra-Separation Axioms

Abstract

The notions of continuity and separation axioms have significance in topological spaces. As a result, there has been a substantial amount of research on continuity and separation axioms, leading to the creation of several modifications of these axioms. In this paper, the concepts of soft slight ω-continuity, soft ultra-Hausdorff, soft ultra-regular, and soft ultra-normal are initiated and investigated. Their characterizations and main features are determined. Also, the links between them and some other relevant concepts are obtained with the help of examples. Moreover, the equivalency between these notions and other related concepts is given under some necessary conditions. In addition, the inverse image of the introduced types of soft separation axioms under soft slight continuity and soft slight ω-continuity is studied, and their reciprocal relationships with respect to their parametric topological spaces are investigated.