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Between the Classes of Soft Open Sets and Soft Omega Open Sets

Author

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  • Samer Al Ghour

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

Abstract

In this paper, we define the class of soft ω 0 -open sets. We show that this class forms a soft topology that is strictly between the classes of soft open sets and soft ω -open sets, and we provide some sufficient conditions for the equality of the three classes. In addition, we show that soft closed soft ω -open sets are soft ω 0 -open sets in soft Lindelof soft topological spaces. Moreover, we study the correspondence between soft ω 0 -open sets in soft topological spaces and ω 0 -open sets in topological spaces. Furthermore, we investigate the relationships between the soft α -open sets (respectively, soft regular open sets, soft β -open sets) of a given soft anti-locally countable soft topological space and the soft α -open sets (respectively, soft regular open sets, soft β -open sets) of the soft topological space of soft ω 0 -open sets generated by it. Finally, we introduce ω 0 -regularity in topological spaces via ω 0 -open sets, which is strictly between regularity and ω -regularity, and we also introduce soft ω 0 -regularity in soft topological spaces via soft ω 0 -open sets, which is strictly between soft regularity and soft ω -regularity. We investigate relationships regarding ω 0 -regularity and soft ω 0 -regularity. Moreover, we study the correspondence between soft ω 0 -regularity in soft topological spaces and ω 0 -regularity in topological spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:719-:d:757655
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    References listed on IDEAS

    as
    1. Metin Akdag & Alkan Ozkan, 2014. "Soft -Open Sets and Soft -Continuous Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    2. Samer Al Ghour, 2021. "Weaker Forms of Soft Regular and Soft T 2 Soft Topological Spaces," Mathematics, MDPI, vol. 9(17), pages 1-13, September.
    3. Tareq M. Al-shami & LjubiÅ¡a D. R. KoÄ inac & Ali Jaballah, 2020. "Nearly Soft Menger Spaces," Journal of Mathematics, Hindawi, vol. 2020, pages 1-9, May.
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    Citations

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    Cited by:

    1. 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.
    2. 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.

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