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On Primal Soft Topology

Author

Listed:
  • 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)

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.

Suggested Citation

  • Tareq M. Al-shami & Zanyar A. Ameen & Radwan Abu-Gdairi & Abdelwaheb Mhemdi, 2023. "On Primal Soft Topology," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2329-:d:1148608
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    References listed on IDEAS

    as
    1. Tareq M. Al-shami & José Carlos R. Alcantud & A. A. Azzam, 2022. "Two New Families of Supra-Soft Topological Spaces Defined by Separation Axioms," Mathematics, MDPI, vol. 10(23), pages 1-18, November.
    2. Tareq M. Al-shami, 2021. "New Soft Structure: Infra Soft Topological Spaces," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-12, July.
    3. Tareq M. Al-shami & Huseyin Isik, 2021. "Homeomorphism and Quotient Mappings in Infrasoft Topological Spaces," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, August.
    4. José Carlos R. Alcantud, 2020. "Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies," Mathematics, MDPI, vol. 8(5), pages 1-12, April.
    5. Tareq M. Al-shami & Abdelwaheb Mhemdi & Radwan Abu-Gdairi, 2023. "A Novel Framework for Generalizations of Soft Open Sets and Its Applications via Soft Topologies," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    6. Tareq M. Al-shami & El-Sayed A. Abo-Tabl, 2021. "Connectedness and Local Connectedness on Infra Soft Topological Spaces," Mathematics, MDPI, vol. 9(15), pages 1-13, July.
    7. Athar Kharal & B. Ahmad, 2011. "Mappings On Soft Classes," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 471-481.
    Full references (including those not matched with items on IDEAS)

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