Between the Classes of Soft Open Sets and Soft Omega 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, 2022, vol. 10, issue 5, 1-14

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

Keywords: soft ? -open sets; ? 0 -open sets; soft anti-locally countable; soft regularity; soft ? -regularity; soft generated soft topological spaces; soft induced topological spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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