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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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