Soft Weakly Quasi-Continuous Functions Between Soft Topological Spaces

Abstract

As an extension of quasi-continuity in general topology, we define soft quasi-continuity. We show that this notion is equivalent to the known notion of soft semi-continuity. Next, we define soft weak quasi-continuity. With the help of examples, we prove that soft weak quasi-continuity is strictly weaker than both soft semi-continuity and soft weak continuity. We introduce many characterizations of soft weak quasi-continuity. Moreover, we study the relationship between soft quasi-continuity and weak quasi-continuity with their analogous notions in general topology. Furthermore, we show that soft regularity of the co-domain of a soft function is a sufficient condition for equivalence between soft semi-continuity and soft weakly quasi-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and soft graph theorems in terms of soft weak quasi-continuity.