Minimal Soft Topologies

Zanyar A. Ameen () and Samer Al Ghour
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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

New Mathematics and Natural Computation (NMNC), 2023, vol. 19, issue 01, 19-31

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.

Keywords: Minimal soft topology; minimal soft T0; minimal soft T1; minimal soft T2; minimal soft regular; minimal soft normal (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S1793005722500466

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