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On Soft ω δ -Open Sets and Some Decomposition Theorems

Author

Listed:
  • Dina Abuzaid

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

  • Samer Al-Ghour

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

  • Monia Naghi

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

Abstract

In this paper, we present a novel family of soft sets named “soft ω δ -open sets”. We find that this class constitutes a soft topology that lies strictly between the soft topologies of soft δ -open sets and soft ω 0 -open sets. Also, we introduce certain sufficient conditions for the equivalence between this new soft topology and several existing soft topologies. Moreover, we verify several relationships that contain soft covering properties, such as soft compactness and soft Lindelofness, which are related to this new soft topology. Furthermore, in terms of the soft interior operator in certain soft topologies, we define four classes of soft sets. Via them, we obtain new decomposition theorems for soft δ -openness and soft θ -openness, and we characterize the soft topological spaces that have the soft “semi-regularization property”. In addition, via soft ω δ -open sets, we introduce and investigate a new class of soft functions named “soft ω δ -continuous functions”. Finally, we look into the connections between the newly proposed soft concepts and their counterparts in classical topological spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:924-:d:1361217
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    References listed on IDEAS

    as
    1. 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.
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