IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i24p3168-d698233.html
   My bibliography  Save this article

Soft Semi ω -Open Sets

Author

Listed:
  • Samer Al Ghour

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

Abstract

In this paper, we introduce the class of soft semi ω -open sets of a soft topological space ( X , τ , A ) , using soft ω -open sets. We show that the class of soft semi ω -open sets contains both the soft topology τ ω and the class of soft semi-open sets. Additionally, we define soft semi ω -closed sets as the class of soft complements of soft semi ω -open sets. We present here a study of the properties of soft semi ω -open sets, especially in ( X , τ , A ) and ( X , τ ω , A ) . In particular, we prove that the class of soft semi ω -open sets is closed under arbitrary soft union but not closed under finite soft intersections; we also study the correspondence between the soft topology of soft semi ω -open sets of a soft topological space and their generated topological spaces and vice versa. In addition to these, we introduce the soft semi ω -interior and soft semi ω -closure operators via soft semi ω -open and soft semi ω -closed sets. We prove several equations regarding these two new soft operators. In particular, we prove that these operators can be calculated using other usual soft operators in both of ( X , τ , A ) and ( X , τ ω , A ) , and some equations focus on soft anti-locally countable soft topological spaces.

Suggested Citation

  • Samer Al Ghour, 2021. "Soft Semi ω -Open Sets," Mathematics, MDPI, vol. 9(24), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3168-:d:698233
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/24/3168/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/24/3168/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sagvan Y. Musa & Baravan A. Asaad, 2021. "Bipolar Hypersoft Sets," Mathematics, MDPI, vol. 9(15), pages 1-15, August.
    2. 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.
    3. 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.
    4. T. M. Al-shami & Ching-Feng Wen, 2021. "Compactness on Soft Topological Ordered Spaces and Its Application on the Information System," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, January.
    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. 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.
    2. Sagvan Y. Musa & Baravan A. Asaad, 2021. "Bipolar Hypersoft Sets," Mathematics, MDPI, vol. 9(15), pages 1-15, August.
    3. 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.
    4. 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.
    5. Tatiana Pedraza & Jesús Rodríguez-López, 2020. "Aggregation of L -Probabilistic Quasi-Uniformities," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    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. Muhammad Saeed & Muhammad Ahsan & Muhammad Haris Saeed & Atiqe Ur Rahman & Asad Mehmood & Mazin Abed Mohammed & Mustafa Musa Jaber & Robertas Damaševičius, 2022. "An Optimized Decision Support Model for COVID-19 Diagnostics Based on Complex Fuzzy Hypersoft Mapping," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    8. 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.
    9. 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.
    10. 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:24:p:3168-:d:698233. 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.