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Minimal Soft Topologies

Author

Listed:
  • Zanyar A. Ameen

    (Department of Mathematics, College of Science, University of Duhok, Duhok 42001, Iraq)

  • Samer Al Ghour

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

Abstract

A collection of all soft topologies over a fixed universe forms a complete lattice. One might ask: what will be the structure of minimal or maximal topologies in this lattice concerning specific topological properties? We know that the soft discrete topology is maximal soft Ti-spaces, for i = 0, 1,…, 4, in terms of the given soft point theory. As a result, we find it interesting to study the construction of minimal soft Ti topologies. We show that the minimal soft T0 is a nested soft topology whose base is the complements of all soft point closures. The minimal soft T1 is the cofinite soft topology. The minimal soft T2 (respectively, T3) is a soft topology in which each soft open (respectively, soft regular) filter base has only one adherent soft point and is convergent. Finally, the minimal soft T4 topologies are subclasses of soft compact topologies.

Suggested Citation

  • Zanyar A. Ameen & Samer Al Ghour, 2023. "Minimal Soft Topologies," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 19-31, March.
    • Handle: RePEc:wsi:nmncxx:v:19:y:2023:i:01:n:s1793005722500466
    DOI: 10.1142/S1793005722500466
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