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Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

Author

Listed:
  • Arif Mehmood

    (Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan)

  • Mohammed M. Al-Shomrani

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

  • Muhammad Asad Zaighum

    (Department of Mathematics & Statistics, Riphah International University, Sector I-14, Islamabad 44000, Pakistan)

  • Saleem Abdullah

    (Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan)

Abstract

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is ( space if each coordinate space is soft space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

Suggested Citation

  • Arif Mehmood & Mohammed M. Al-Shomrani & Muhammad Asad Zaighum & Saleem Abdullah, 2020. "Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points," Mathematics, MDPI, vol. 8(12), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2100-:d:450150
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    References listed on IDEAS

    as
    1. Arif Mehmood Khattak & Gulzar Ali Khan & Younis Khan & Muhammad Ishfaq Khattak & Fahad Jamal, 2018. "Characterization Of Soft B Separation Axioms In Soft Bi-Topological Spaces," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 2(2), pages 11-17, January.
    2. Güzide Şenel, 2016. "A New Approach to Hausdorff Space Theory via the Soft Sets," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-6, September.
    3. Metin Akdag & Alkan Ozkan, 2014. "Soft -Open Sets and Soft -Continuous Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, February.
    4. Kalayathankal, Sunny Joseph & Suresh Singh, G., 2010. "A fuzzy soft flood alarm model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 887-893.
    Full references (including those not matched with items on IDEAS)

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