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Open AccessArticle

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

BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, Spain
Mathematics 2020, 8(5), 672; https://doi.org/10.3390/math8050672
Received: 14 April 2020 / Revised: 26 April 2020 / Accepted: 27 April 2020 / Published: 29 April 2020
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. View Full-Text
Keywords: soft open base; soft topology; topology; separability; second countability axiom soft open base; soft topology; topology; separability; second countability axiom
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MDPI and ACS Style

Alcantud, J.C.R. Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies. Mathematics 2020, 8, 672. https://doi.org/10.3390/math8050672

AMA Style

Alcantud JCR. Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies. Mathematics. 2020; 8(5):672. https://doi.org/10.3390/math8050672

Chicago/Turabian Style

Alcantud, José C.R. 2020. "Soft Open Bases and a Novel Construction of Soft Topologies from Bases for Topologies" Mathematics 8, no. 5: 672. https://doi.org/10.3390/math8050672

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