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Soft ω p -Open Sets and Soft ω p -Continuity in Soft Topological Spaces

Author

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  • Samer Al Ghour

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

Abstract

We define soft ω p -openness as a strong form of soft pre-openness. We prove that the class of soft ω p -open sets is closed under soft union and do not form a soft topology, in general. We prove that soft ω p -open sets which are countable are soft open sets, and we prove that soft pre-open sets which are soft ω -open sets are soft ω p -open sets. In addition, we give a decomposition of soft ω p -open sets in terms of soft open sets and soft ω -dense sets. Moreover, we study the correspondence between the soft topology soft ω p -open sets in a soft topological space and its generated topological spaces, and vice versa. In addition to these, we define soft ω p -continuous functions as a new class of soft mappings which lies strictly between the classes of soft continuous functions and soft pre-continuous functions. We introduce several characterizations for soft pre-continuity and soft ω p -continuity. Finally, we study several relationships related to soft ω p -continuity.

Suggested Citation

  • Samer Al Ghour, 2021. "Soft ω p -Open Sets and Soft ω p -Continuity in Soft Topological Spaces," Mathematics, MDPI, vol. 9(20), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2632-:d:659547
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    References listed on IDEAS

    as
    1. Tareq M. Al-shami & Ahmed Mostafa Khalil, 2021. "Bipolar Soft Sets: Relations between Them and Ordinary Points and Their Applications," Complexity, Hindawi, vol. 2021, pages 1-14, January.
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