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

Ismail Ibedou (), Salah E. Abbas and Mesfer H. Alqahtani
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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

Mathematics, 2025, vol. 13, issue 11, 1-16

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.

Keywords: topological space; separation axioms; connectedness; rough sets; approximation spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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