On some weaker forms of soft continuity and their decomposition theorems

In this paper, we employ soft omega(0)-open sets to establish four new classes of soft functions in STSs: soft omega(0)-continuity, soft weak omega(0)-continuity, soft w*-continuity, and soft w*-omega(0)-continuity. We show that soft weak omega(0)-continuity and soft w*-omega(0)-continuity are distinct notions, each of which is strictly weaker than soft omega(0)-continuity. Furthermore, we get a soft omega(0)-continuity decomposition theorem via both weak omega(0)-continuity and soft w*-omega(0)-continuity. In addition, we demonstrate that soft w*-continuity is precisely between soft continuity and soft w*-omega(0)-continuity. We further show that soft w* -continuity and soft weak continuity are distinct concepts. In addition, we develop a soft continuity decomposition theorem via soft w* -continuity and soft weak continuity. Finally, we examine the connection between our new soft topological ideas and their corresponding topological concepts. Include keywords, mathematical subject classification numbers as needed.