Soft Semi ω -Open Sets

Samer Al Ghour
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Samer Al Ghour: Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan

Mathematics, 2021, vol. 9, issue 24, 1-12

Abstract: In this paper, we introduce the class of soft semi ω -open sets of a soft topological space ( X , τ , A ) , using soft ω -open sets. We show that the class of soft semi ω -open sets contains both the soft topology τ ω and the class of soft semi-open sets. Additionally, we define soft semi ω -closed sets as the class of soft complements of soft semi ω -open sets. We present here a study of the properties of soft semi ω -open sets, especially in ( X , τ , A ) and ( X , τ ω , A ) . In particular, we prove that the class of soft semi ω -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 ω -open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi ω -interior and soft semi ω -closure operators via soft semi ω -open and soft semi ω -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 , τ , A ) and ( X , τ ω , A ) , and some equations focus on soft anti-locally countable soft topological spaces.

Keywords: soft ?-open; soft semi-open; soft semi interior; soft semi interior; soft generated soft topological space; soft induced topological spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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