IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2100-d450150.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2100/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/12/2100/
    Download Restriction: no
    ---><---

    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Samer Al Ghour & Hanan Al-Saadi, 2023. "Soft ω - θ -Continuous and Soft Weakly θ ω -Continuous Mappings," Mathematics, MDPI, vol. 11(19), pages 1-15, September.
    2. R. Rajesh & Chandrasekharan Rajendran, 2019. "Grey- and rough-set-based seasonal disaster predictions: an analysis of flood data in India," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 97(1), pages 395-435, May.
    3. 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.
    4. Tahir Ayaz & Arif Mehmood Khattak & Nisar Ahmad, 2018. "Supra Soft R-Separation Axioms," Acta Scientifica Malaysia (ASM), Zibeline International Publishing, vol. 2(2), pages 27-31, August.
    5. 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.
    6. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2100-:d:450150. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.