Soft ω-regular open sets and soft nearly Lindelöfness

Samer Al Ghour

doi:10.1016/j.heliyon.2022.e09954

Soft ω-regular open sets and soft nearly Lindelöfness

Heliyon. 2022 Jul 18;8(7):e09954. doi: 10.1016/j.heliyon.2022.e09954. eCollection 2022 Jul.

Author

Samer Al Ghour¹

Affiliation

¹ Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan.

Abstract

In this paper, we define the notion of "soft ω-regular openness," which lies exactly between "soft regular openness" and "soft ω-openness." Through soft ω-regular open sets, we introduce the notions of soft semi ω-regularity as a weaker form of soft semi regularity and soft almost ω-regularity as a strong form of soft almost regularity. We prove that soft ω-regular open sets of a soft topological space form a soft topology. Also, we prove that soft semi ω-regularity and soft almost ω-regularity are independent notions. In addition, we reveal the relationships between soft topology and classical (parametric) topology. Finally, we characterize soft nearly Lindelöfness and improve several results related to soft nearly Lindelöfness using the concept of soft ω-regular open sets.

Keywords: Soft almost regular; Soft generated soft topological space; Soft induced topological spaces; Soft nearly Lindelöf; Soft regular open; Soft semi regular.