Soft ωs-irresoluteness and soft pre-ωs-openness insoft topological spaces

Abstract

We use soft ωs-open sets to define soft ωs-irresoluteness, soft ωs-openness, and soft pre-ωs-openness as three new classes of soft mappings. We give several characterizations for each of them, specially via soft ωs-closure and soft ωs-interior soft operators. With the help of examples, we study several relationships regarding these three notions and their related known notions. In particular, we show that soft ωs-irresoluteness is strictly weaker than soft ωs-continuity, soft ωs-openness lies strictly between soft openness and soft semi-openness, pre-ωs-openness is strictly weaker than ωs-openness, soft ωs-irresoluteness is independent of each of soft continuity and soft irresoluteness, soft pre-ωs-openness is independent of each of soft openness and soft pre-semi-openness, soft ωs-irresoluteness and soft continuity (resp. soft irresoluteness) are equivalent for soft mappings between soft locally countable (resp. soft anti-locally countable) soft topological spaces, and soft pre-ωs-openness and soft pre-semi-continuity are equivalent for soft mappings between soft locally countable soft topological spaces. Moreover, we study the relationship between our new concepts in soft topological spaces and their topological analog.