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Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies

Author

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  • José Carlos R. Alcantud

    (BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain)

Abstract

Soft topology studies a structure on the collection of all soft sets on a given set of alternatives (the relevant attributes being fixed). It is directly inspired by the axioms of a topological space. This paper contributes to the theoretical bases of soft topology in various ways. We extend a general construction of soft topologies from topologies on the set of alternatives in two different directions. An extensive discussion with criteria about what a soft counterpart of “topological separability” should satisfy is also given. The interactions of the properties that arise with separability, and of second-countability and its soft counterpart, are studied under the general mechanisms that generate soft topological spaces. The first non-trivial examples of soft second-countable soft topological spaces are produced as a consequence.

Suggested Citation

  • José Carlos R. Alcantud, 2020. "Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies," Mathematics, MDPI, vol. 8(5), pages 1-12, April.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:672-:d:352207
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    Citations

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    Cited by:

    1. 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.
    2. Basit Ali & Naeem Saleem & Nozara Sundus & Sana Khaleeq & Muhammad Saeed & Reny George, 2022. "A Contribution to the Theory of Soft Sets via Generalized Relaxed Operations," Mathematics, MDPI, vol. 10(15), pages 1-14, July.

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