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Soft Weakly Quasi-Continuous Functions Between Soft Topological Spaces

Author

Listed:
  • Samer Al-Ghour

    (Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan)

  • Dina Abuzaid

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Monia Naghi

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

As an extension of quasi-continuity in general topology, we define soft quasi-continuity. We show that this notion is equivalent to the known notion of soft semi-continuity. Next, we define soft weak quasi-continuity. With the help of examples, we prove that soft weak quasi-continuity is strictly weaker than both soft semi-continuity and soft weak continuity. We introduce many characterizations of soft weak quasi-continuity. Moreover, we study the relationship between soft quasi-continuity and weak quasi-continuity with their analogous notions in general topology. Furthermore, we show that soft regularity of the co-domain of a soft function is a sufficient condition for equivalence between soft semi-continuity and soft weakly quasi-continuity. Furthermore, we provide several results of soft composition, restrictions, preservation, and soft graph theorems in terms of soft weak quasi-continuity.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:20:p:3280-:d:1502246
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    References listed on IDEAS

    as
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    2. 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.
    3. Samer Al Ghour, 2022. "Between the Classes of Soft Open Sets and Soft Omega Open Sets," Mathematics, MDPI, vol. 10(5), pages 1-14, February.
    4. Metin Akdag & Alkan Ozkan, 2014. "Soft -Open Sets and Soft -Continuous Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    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.
    6. Xia, Yude & Wang, Jing & Meng, Bo & Chen, Xiangyong, 2020. "Further results on fuzzy sampled-data stabilization of chaotic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    Full references (including those not matched with items on IDEAS)

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