Soft Semi ω-Open Sets

In this paper, we introduce the class of soft semi omega-open sets of a soft topological space (X,tau,A), using soft omega-open sets. We show that the class of soft semi omega-open sets contains both the soft topology tau omega and the class of soft semi-open sets. Additionally, we define soft semi omega-closed sets as the class of soft complements of soft semi omega-open sets. We present here a study of the properties of soft semi omega-open sets, especially in (X,tau,A) and (X,tau(omega),A). In particular, we prove that the class of soft semi omega-open sets is closed under arbitrary soft union but not closed under finite soft intersections; we also study the correspondence between the soft topology of soft semi omega-open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi omega-interior and soft semi omega-closure operators via soft semi omega-open and soft semi omega-closed sets. We prove several equations regarding these two new soft operators. In particular, we prove that these operators can be calculated using other usual soft operators in both of (X,tau,A) and (X,tau(omega),A), and some equations focus on soft anti-locally countable soft topological spaces.