An Operational Characterization of Soft Topologies by Crisp Topologies

This paper contributes to the expanding literature on soft topology. We first prove that soft topologies can be characterized by crisp topologies. This takes advantage of two connected constructions that produce soft topologies from crisp topologies and vice versa. Both constructions are explicit an...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 14; p. 1656
Main Author Alcantud, José Carlos R.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2021
Subjects
base for a topology
Exports
Food science
Investigations
second-countable space
separability
Set theory
soft topology
Topology
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Summary:This paper contributes to the expanding literature on soft topology. We first prove that soft topologies can be characterized by crisp topologies. This takes advantage of two connected constructions that produce soft topologies from crisp topologies and vice versa. Both constructions are explicit and amenable to mathematical manipulations. Various consequences demonstrate that our theory has far-reaching implications for the development of soft topology and its extensions.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9141656