IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i11p1859-d1670464.html
   My bibliography  Save this article

Defining New Structures on a Universal Set: Diving Structures and Floating Structures

Author

Listed:
  • Ismail Ibedou

    (Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt)

  • Salah E. Abbas

    (Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt)

  • Mesfer H. Alqahtani

    (Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia)

Abstract

This paper introduces new structures ( DV , FL ) on a set Ξ . They will be known as diving structures and floating structures. The pairs ( Ξ , DV ) , ( Ξ , FL ) will be called diving spaces and floating spaces, respectively. These structures are not related to each other and are not related to any of the previous common structures such as topology, ideal, filter, grill or primal. We study some properties to characterize these new notions. Separation axioms and connectedness will be defined in these new spaces. When R is an equivalence relation on Ξ , rough sets in diving spaces and rough sets in floating spaces will also be defined. Thus, ( Ξ , R , DV ) and ( Ξ , R , FL ) are called the diving approximation spaces and the floating approximation spaces, respectively.

Suggested Citation

  • Ismail Ibedou & Salah E. Abbas & Mesfer H. Alqahtani, 2025. "Defining New Structures on a Universal Set: Diving Structures and Floating Structures," Mathematics, MDPI, vol. 13(11), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:11:p:1859-:d:1670464
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/11/1859/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/11/1859/
    Download Restriction: no
    ---><---

    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:13:y:2025:i:11:p:1859-:d:1670464. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.