On some weaker forms of soft continuity and their decomposition theorems

Abstract

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 \(w^{\ast }\) -continuity, and soft \(w^{\ast }\)-\(\omega ^{0}\)-continuity. We show that soft weak \(\omega ^{0}\)-continuity and soft \(w^{\ast }\)-\(\omega ^{0}\) -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 \(w^{\ast }\)-\(\omega ^{0}\)-continuity. In addition, we demonstrate that soft \(w^{\ast }\)-continuity is precisely between soft continuity and soft \( w^{\ast }\)-\(\omega ^{0}\)-continuity. We further show that soft \(w^{\ast }\) -continuity and soft weak continuity are distinct concepts. In addition, we develop a soft continuity decomposition theorem via soft \(w^{\ast }\) -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.