On Primal Soft Topology

Tareq M. Al-shami, Zanyar A. Ameen, Radwan Abu-Gdairi and Abdelwaheb Mhemdi ()
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Tareq M. Al-shami: Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen
Zanyar A. Ameen: Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq
Radwan Abu-Gdairi: Department of Mathematics, Faculty of Science, Zarqa University, Zarqa P.O. Box 13110, Jordan
Abdelwaheb Mhemdi: Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam Bin Abdulaziz University, Riyadh 16273, Saudi Arabia

Mathematics, 2023, vol. 11, issue 10, 1-15

Abstract: In a soft environment, we investigated several (classical) structures such as ideals, filters, grills, etc. It is well known that these structures are applied to expand abstract concepts; in addition, some of them offer a vital tool to address some practical issues, especially those related to improving rough approximation operators and accuracy measures. Herein, we contribute to this line of research by presenting a novel type of soft structure, namely “soft primal”. We investigate its basic properties and describe its behaviors under soft mappings with the aid of some counterexamples. Then, we introduce three soft operators ( · ) ⋄ , C l ⋄ and ( · ) □ inspired by soft primals and explore their main characterizations. We show that C l ⋄ satisfies the soft Kuratowski closure operator, which means that C l ⋄ generates a unique soft topology we call a primal soft topology. Among other obtained results, we elaborate that the set of primal topologies forms a natural class in the lattice of topologies over a universal set and set forth some descriptions for primal soft topology under specific types of soft primals.

Keywords: soft primal; soft grill; primal soft topology; soft base; soft Kuratowski’s closure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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