Soft ω-θ-Continuous and Soft Weakly θω-Continuous Mappings

Abstract

Soft ω-θ-continuity and soft weak-θω-continuity as two new concepts of continuity are presented and investigated. The investigation of the links between these forms of soft mappings and their general topological relatives is given. With the help of examples, it is investigated that soft ω-θ-continuity lies strictly between soft θ-continuity and soft weak-continuity, while soft weak-θω-continuity lies strictly between soft continuity (i.e., soft θω-continuity) and soft weak-continuity. A number of conditions for the equivalence between soft ω-θ-continuity and soft weak continuity (i.e., soft ω-θ-continuity and soft θ-continuity, soft weak-θω-continuity and soft weak-continuity, soft weak-θω-continuity and soft continuity) are obtained. Additionally, soft θ-closure and soft θω-closure operators are used to characterize our new types of soft mappings.