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

Tuǧçe Aydın, Serdar Enginoǧlu () and Ahmet Mollaoǧulları ()
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Tuǧçe Aydın: Department of Mathematics, College of Arts and Sciences, Çanakkale Onsekiz Mart University, Çanakkale, Turkey
Serdar Enginoǧlu: Department of Mathematics, College of Arts and Sciences, Çanakkale Onsekiz Mart University, Çanakkale, Turkey
Ahmet Mollaoǧulları: Department of Mathematics, College of Arts and Sciences, Çanakkale Onsekiz Mart University, Çanakkale, Turkey

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 01, 105-130

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 semi-separation 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.

Keywords: Soft sets; soft topology; soft element; soft semi-open sets; soft semi-separation axioms (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005723500023

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