Clarifying Soft Semi-separation Axioms Using the Concept of Soft Element

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Aydın T., Enginoğlu S.

NEW MATHEMATICS AND NATURAL COMPUTATION, vol.19, no.1, pp.105-130, 2023 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1142/s1793005723500023
  • Journal Name: NEW MATHEMATICS AND NATURAL COMPUTATION
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.105-130
  • Keywords: soft element, soft semi-open sets, soft semi-separation axioms, Soft sets, soft topology
  • Çanakkale Onsekiz Mart University Affiliated: Yes

Abstract

Recently, soft semi-open sets being a generalization of soft open sets and soft topological notions related to them have been studied. However, these studies have not tackled the concept of soft elements. To this end, we conduct a grounding study on soft semi-open sets and investigate soft topological notions through this concept. We then define soft semiseparation axioms in soft topological spaces on a soft set via soft elements. Moreover, we examine the relationships between these spaces and their subspaces. Afterward, we clarify the theoretical section of the study with presented examples and study the relationships between soft semi-separation axioms and soft separation axioms. Finally, we discuss the study’s contributions to the literature and the need for further research.