A Stronger Novel Form of Soft Semi-Open Set

Payman M. Mahmood (), Halgwrd M. Darwesh (), Hardi A. Shareef () and Samer Al Ghour
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Payman M. Mahmood: Department of Mathematics, College of Education for Pure Sciences, University of Kirkuk, Iraq
Halgwrd M. Darwesh: ��Department of Mathematics, College of Science, University of Sulaimani, Kurdistan-Region, Iraq
Hardi A. Shareef: ��Department of Mathematics, College of Science, University of Sulaimani, Kurdistan-Region, Iraq
Samer Al Ghour: ��Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 01, 323-338

Abstract: In this paper, we introduce the concept of a soft Sp-open set. We show that the class of soft Sp-open sets lies strictly between the classes of S̃Sc-open sets (respectively, soft 𠜃-open) and soft semi-open sets. Additionally, we provide several adequate criteria for the equivalence between soft Sp-open sets and each of S̃Sc-open sets and soft semi-open sets. Moreover, we demonstrate that the family of soft Sp-open sets is a supra soft topology. We study the relationships between soft Sp-open sets and other types of soft sets such as soft open, soft pre-open, soft α-open, soft ξ-open, soft δ-open, soft bc-open and soft βc-open. Also, we study the behavior of soft Sp-open sets under some soft operators. Finally, we clarify the correspondence between the classes of soft Sp-open sets in a soft topological space and in its soft topological subspaces.

Keywords: Soft topology; soft semi-open sets; soft pre-closed sets; soft Sp-open sets; soft p-Alexandroff space (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500164

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