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A Novel Framework for Generalizations of Soft Open Sets and Its Applications via Soft Topologies

Author

Listed:
  • Tareq M. Al-shami

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

  • Abdelwaheb Mhemdi

    (Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh 16273, Saudi Arabia)

  • Radwan Abu-Gdairi

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

Abstract

Soft topological spaces (STSs) have received a lot of attention recently, and numerous soft topological ideas have been created from differing viewpoints. Herein, we put forth a new class of generalizations of soft open sets called “weakly soft semi-open subsets” following an approach inspired by the components of a soft set. This approach opens the door to reformulating the existing soft topological concepts and examining their behaviors. First, we deliberate the main structural properties of this class and detect its relationships with the previous generalizations with the assistance of suitable counterexamples. In addition, we probe some features that are obtained under some specific stipulations and elucidate the properties of the forgoing generalizations that are missing in this class. Next, we initiate the interior and closure operators with respect to the classes of weakly soft semi-open and weakly soft semi-closed subsets and look at some of their fundamental characteristics. Ultimately, we pursue the concept of weakly soft semi-continuity and furnish some of its descriptions. By a counterexample, we elaborate that some characterizations of soft continuous functions are invalid for weakly soft semi-continuous functions.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:840-:d:1060317
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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. Metin Akdag & Alkan Ozkan, 2014. "Soft -Open Sets and Soft -Continuous Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    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. T. M. Al-shami & Ching-Feng Wen, 2021. "Compactness on Soft Topological Ordered Spaces and Its Application on the Information System," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, January.
    5. 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.
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    Citations

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    Cited by:

    1. Ahmad Al-Omari & Wafa Alqurashi, 2023. "Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces," Mathematics, MDPI, vol. 11(22), pages 1-10, November.
    2. Zanyar A. Ameen & Tareq M. Al-shami & Radwan Abu-Gdairi & Abdelwaheb Mhemdi, 2023. "The Relationship between Ordinary and Soft Algebras with an Application," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    3. Sandeep Kaur & Tareq M. Al-shami & Alkan Özkan & M. Hosny, 2023. "A New Approach to Soft Continuity," Mathematics, MDPI, vol. 11(14), pages 1-11, July.
    4. 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.
    5. Samer Al-Ghour & Dina Abuzaid & Monia Naghi, 2024. "Soft Weakly Quasi-Continuous Functions Between Soft Topological Spaces," Mathematics, MDPI, vol. 12(20), pages 1-19, October.
    6. Dina Abuzaid & Samer Al-Ghour & Monia Naghi, 2024. "On Soft ω δ -Open Sets and Some Decomposition Theorems," Mathematics, MDPI, vol. 12(6), pages 1-14, March.
    7. Samer Al Ghour & Hanan Al-Saadi, 2023. "Soft ω - θ -Continuous and Soft Weakly θ ω -Continuous Mappings," Mathematics, MDPI, vol. 11(19), pages 1-15, September.
    8. Samer Al Ghour & Hanan Al-Saadi, 2023. "Soft Slight Omega-Continuity and Soft Ultra-Separation Axioms," Mathematics, MDPI, vol. 11(15), pages 1-17, July.

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