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

• Published in: Mathematics (Basel) Vol. 10; no. 5; p. 719
• Main Author: Al Ghour, Samer
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2022
• Subjects: Fuzzy sets; Game theory; Mathematics; Regularity; Set theory; soft anti-locally countable; soft generated soft topological spaces; soft regularity; soft ω-open sets; soft ω-regularity; Topology; ω0-open sets
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10050719

In this paper, we define the class of soft ω0-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 ω0-open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω0-open sets in soft topological spaces and ω0-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 ω0-open sets generated by it. Finally, we introduce ω0-regularity in topological spaces via ω0-open sets, which is strictly between regularity and ω-regularity, and we also introduce soft ω0-regularity in soft topological spaces via soft ω0-open sets, which is strictly between soft regularity and soft ω-regularity. We investigate relationships regarding ω0-regularity and soft ω0-regularity. Moreover, we study the correspondence between soft ω0-regularity in soft topological spaces and ω0-regularity in topological spaces.