Between the Classes of Soft Open Sets and Soft Omega Open Sets

In this paper, we define the class of soft omega(0)-open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft omega-open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft omega-open sets are soft omega 0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft omega(0)-open sets in soft topological spaces and omega 0-open sets in topological spaces. Furthermore, we investigate the relationships between the soft alpha-open sets (respectively, soft regular open sets, soft beta-open sets) of a given soft anti-locally countable soft topological space and the soft alpha-open sets (respectively, soft regular open sets, soft beta-open sets) of the soft topological space of soft omega(0)-open sets generated by it. Finally, we introduce omega 0-regularity in topological spaces via omega 0-open sets, which is strictly between regularity and omega-regularity, and we also introduce soft omega(0)-regularity in soft topological spaces via soft omega(0)-open sets, which is strictly between soft regularity and soft omega-regularity. We investigate relationships regarding omega(0)-regularity and soft omega(0)-regularity. Moreover, we study the correspondence between soft omega(0)-regularity in soft topological spaces and omega 0-regularity in topological spaces.