On Soft <i>ω_δ</i>-Open Sets and Some Decomposition Theorems

Abstract

In this paper, we present a novel family of soft sets named “soft ωδ-open sets”. We find that this class constitutes a soft topology that lies strictly between the soft topologies of soft δ-open sets and soft ω0-open sets. Also, we introduce certain sufficient conditions for the equivalence between this new soft topology and several existing soft topologies. Moreover, we verify several relationships that contain soft covering properties, such as soft compactness and soft Lindelofness, which are related to this new soft topology. Furthermore, in terms of the soft interior operator in certain soft topologies, we define four classes of soft sets. Via them, we obtain new decomposition theorems for soft δ-openness and soft θ-openness, and we characterize the soft topological spaces that have the soft “semi-regularization property”. In addition, via soft ωδ-open sets, we introduce and investigate a new class of soft functions named “soft ωδ-continuous functions”. Finally, we look into the connections between the newly proposed soft concepts and their counterparts in classical topological spaces.

Keywords

• soft <i>δ</i>-open sets
• soft <i>θ</i>-open sets
• soft <i>ω</i>⁰-open sets
• super-continuity
• soft generated soft topological spaces