IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2153-d628648.html
   My bibliography  Save this article

Weaker Forms of Soft Regular and Soft T 2 Soft Topological Spaces

Author

Listed:
  • Samer Al Ghour

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

Abstract

Soft ω -local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft ω -regularity as a weaker form of both soft regularity and soft ω -local indiscreetness is defined and investigated. Additionally, soft ω - T 2 as a new soft topological property that lies strictly between soft T 2 and soft T 1 is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft ω -locally indiscreetness (resp. soft ω -regularity) and soft locally indiscreetness (resp. soft ω -regularity). Additionally, it is proved that the induced topological spaces of a soft ω -locally indiscrete (resp. soft ω -regular, soft ω - T 2 ) soft topological space are (resp. ω -regular, ω - T 2 ) topological spaces. Additionally, it is proved that the generated soft topological space of a family of ω -locally indiscrete (resp. ω -regular, ω - T 2 ) topological spaces is soft ω -locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft ω -regular and soft ω - T 2 soft topological spaces are obtained. Moreover, it is proved that soft ω -regular and soft ω - T 2 are hereditarily under soft subspaces.

Suggested Citation

  • 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.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2153-:d:628648
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2153/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/9/17/2153/
    Download Restriction: no
    ---><---

    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.
    2. Tareq M. Al-shami & Ljubiša D. R. Kočinac & Baravan A. Asaad, 2020. "Sum of Soft Topological Spaces," Mathematics, MDPI, vol. 8(6), pages 1-12, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    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. Sagvan Y. Musa & Baravan A. Asaad, 2021. "Bipolar Hypersoft Sets," Mathematics, MDPI, vol. 9(15), pages 1-15, August.
    2. Samer Al Ghour, 2021. "Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts," Mathematics, MDPI, vol. 9(15), pages 1-14, July.
    3. Samer Al Ghour, 2021. "Soft Semi ω -Open Sets," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    4. Tatiana Pedraza & Jesús Rodríguez-López, 2020. "Aggregation of L -Probabilistic Quasi-Uniformities," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    5. Zanyar A. Ameen & Tareq M. Al-shami & Radwan Abu-Gdairi & Abdelwaheb Mhemdi, 2023. "The Relationship between Ordinary and Soft Algebras with an Application," Mathematics, MDPI, vol. 11(9), pages 1-12, April.
    6. José Carlos R. Alcantud & Tareq M. Al-shami & A. A. Azzam, 2021. "Caliber and Chain Conditions in Soft Topologies," Mathematics, MDPI, vol. 9(19), pages 1-15, September.
    7. Nagarajan Kalaivani & Khaleel Fayaz Ur Rahman & Lenka Čepová & Robert Čep, 2022. "On Grill S β -Open Set in Grill Topological Spaces," Mathematics, MDPI, vol. 10(23), pages 1-9, December.
    8. 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.

    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:9:y:2021:i:17:p:2153-:d:628648. 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.