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New Operators Inspired by Ideal Topological Spaces and Their Application to Establishing Topology and Compatibility Property

Author

Listed:
  • Murad Özkoç
  • Faical Yacine Issaka
  • Tareq M. Al-Shami
  • Alaa M. Abd El-Latif

Abstract

In this article at hand, we employ the sharp operator to set up two novel operators via ideal topological spaces, namely, Δ‐operator and clΔ‐operators, and demonstrate how they interact with other ideas and properties. To prove some invalid relationships and further illustrate our discussion of some of their properties, we provide some elucidative examples. Then, we show that the operator clΔ turns out to be a Kuratowski closure operator; therefore, we use clΔ‐operator to create a new topology that is incomparable with the old one. Furthermore, we investigate the core properties of the operator of ∇‐sharp local function and make use of it to describe a topology TΔ established by clΔ‐operator. Finally, we present the concept of ♯‐compatibility and explore its main characterizations. We also reveal the relationship between compatibility and ♯‐compatibility supported with some counterexamples.

Suggested Citation

  • Murad Özkoç & Faical Yacine Issaka & Tareq M. Al-Shami & Alaa M. Abd El-Latif, 2025. "New Operators Inspired by Ideal Topological Spaces and Their Application to Establishing Topology and Compatibility Property," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:4220174
    DOI: 10.1155/jom/4220174
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    References listed on IDEAS

    as
    1. Ahmad Al-Omari & Mesfer H. Alqahtani, 2023. "Primal Structure with Closure Operators and Their Applications," Mathematics, MDPI, vol. 11(24), pages 1-13, December.
    2. Murad Özkoç & Faical Yacine Issaka & Tareq M. Al-shami & Anwar J. Fawakhreh, 2025. "Connectedness via Primal Topological Spaces With Applications of Primals to Rough Operators," Journal of Mathematics, Hindawi, vol. 2025, pages 1-12, September.
    3. Mona Hosny & Tareq M. Al-shami & Abdelwaheb Mhemdi, 2022. "Rough Approximation Spaces via Maximal Union Neighborhoods and Ideals with a Medical Application," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    4. Murad Özkoç & Faical Yacine Issaka & Tareq M. Al-shami & Anwar J. Fawakhreh, 2025. "Connectedness via Primal Topological Spaces With Applications of Primals to Rough Operators," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    5. Mona Hosny & Tareq M. Al-shami & Abdelwaheb Mhemdi & Yongqiang Fu, 2022. "Rough Approximation Spaces via Maximal Union Neighborhoods and Ideals with a Medical Application," Journal of Mathematics, Hindawi, vol. 2022, pages 1-17, September.
    6. Tareq M. Al-shami & Zanyar A. Ameen & Radwan Abu-Gdairi & Abdelwaheb Mhemdi, 2023. "On Primal Soft Topology," Mathematics, MDPI, vol. 11(10), pages 1-15, May.
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    1. Murad Özkoç & Faical Yacine Issaka & Tareq M. Al-shami & Anwar J. Fawakhreh, 2025. "Connectedness via Primal Topological Spaces With Applications of Primals to Rough Operators," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).

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