Soft ω-Weak Continuity between Soft Topological Spaces

We define soft w -weak continuity as a new soft continuity notion, which is strictly weaker than the soft w -continuity and soft weak continuity. We present two characterizations and two composition theorems for the soft w -weak continuity. Moreover, via soft w -weak continuity, we give several preservation theorems related to soft connectedness and soft separation axioms. Additionally, we introduce w* - w -continuous functions as a new class of soft functions strictly containing a class of soft w -continuous functions. We show that soft w -weak continuity and soft w* - w -continuities are independent notions, and use them to obtain a decomposition theorem for the soft w -continuity. Finally, we study the relationships between our new soft notions and their analogs in general topology.