Soft ωp-Open Sets and Soft ωp-Continuity in Soft Topological Spaces

We define soft omega p-openness as a strong form of soft pre-openness. We prove that the class of soft omega p-open sets is closed under soft union and do not form a soft topology, in general. We prove that soft omega p-open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft omega-open sets are soft omega p-open sets. In addition, we give a decomposition of soft omega p-open sets in terms of soft open sets and soft omega-dense sets. Moreover, we study the correspondence between the soft topology soft omega p-open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft omega p-continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft omega p-continuity. Finally, we study several relationships related to soft omega p-continuity.</p>