On Primal Soft Topology

Author:

Al-shami Tareq M.1ORCID,Ameen Zanyar A.2ORCID,Abu-Gdairi Radwan3ORCID,Mhemdi Abdelwaheb4ORCID

Affiliation:

1. Department of Mathematics, Sana’a University, Sana’a P.O. Box 1247, Yemen

2. Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq

3. Department of Mathematics, Faculty of Science, Zarqa University, Zarqa P.O. Box 13110, Jordan

4. Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam Bin Abdulaziz University, Riyadh 16273, Saudi Arabia

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 (·)⋄, Cl⋄ and (·)□ inspired by soft primals and explore their main characterizations. We show that Cl⋄ satisfies the soft Kuratowski closure operator, which means that Cl⋄ 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.

Funder

Prince Sattam bin Abdulaziz University

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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