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AIMS Mathematics

2024, Volume 9, Issue 3: 6379-6410. doi: 10.3934/math.2024311
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Research article

Soft closure spaces via soft ideals

  • 1.
    Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Saudi Arabia
  • 2.
    Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
  • 3.
    Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
  • Received: 13 December 2023 Revised: 25 January 2024 Accepted: 29 January 2024 Published: 05 February 2024

  • MSC : 54A05, 54D10, 54D05, 54A10, 54C40

  • This paper was devoted to defining new soft closure operators via soft relations and soft ideals, and consequently new soft topologies. The resulting space is a soft ideal approximation. Many of the well known topological concepts were given in the soft set-topology. Particularly, it introduced the notations of soft accumulation points, soft continuous functions, soft separation axioms, and soft connectedness. Counterexamples were introduced to interpret the right implications. Also, a practical application of the new soft approximations was explained by an example of a real-life problem.

    Citation: Rehab Alharbi, S. E. Abbas, E. El-Sanowsy, H. M. Khiamy, Ismail Ibedou. Soft closure spaces via soft ideals[J]. AIMS Mathematics, 2024, 9(3): 6379-6410. doi: 10.3934/math.2024311

    Related Papers:

  • This paper was devoted to defining new soft closure operators via soft relations and soft ideals, and consequently new soft topologies. The resulting space is a soft ideal approximation. Many of the well known topological concepts were given in the soft set-topology. Particularly, it introduced the notations of soft accumulation points, soft continuous functions, soft separation axioms, and soft connectedness. Counterexamples were introduced to interpret the right implications. Also, a practical application of the new soft approximations was explained by an example of a real-life problem.


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