An Operational Characterization of Soft Topologies by Crisp Topologies

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
Main Author: José Carlos R. Alcantud
Format: Article
Language:English
Published: MDPI AG 2021-07-01
Series:Mathematics
Subjects:
soft topology
topology
base for a topology
second-countable space
separability
Online Access:https://www.mdpi.com/2227-7390/9/14/1656
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spelling doaj-a28aa4f250de4a4da2a437c517ba86a42021-07-23T13:52:30ZengMDPI AGMathematics2227-73902021-07-0191656165610.3390/math9141656An Operational Characterization of Soft Topologies by Crisp TopologiesJosé Carlos R. Alcantud0BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, E37007 Salamanca, SpainThis 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.https://www.mdpi.com/2227-7390/9/14/1656soft topologytopologybase for a topologysecond-countable spaceseparability
collection DOAJ
language English
format Article
sources DOAJ
author José Carlos R. Alcantud
spellingShingle José Carlos R. Alcantud
An Operational Characterization of Soft Topologies by Crisp Topologies
Mathematics
soft topology
topology
base for a topology
second-countable space
separability
author_facet José Carlos R. Alcantud
author_sort José Carlos R. Alcantud
title An Operational Characterization of Soft Topologies by Crisp Topologies
title_short An Operational Characterization of Soft Topologies by Crisp Topologies
title_full An Operational Characterization of Soft Topologies by Crisp Topologies
title_fullStr An Operational Characterization of Soft Topologies by Crisp Topologies
title_full_unstemmed An Operational Characterization of Soft Topologies by Crisp Topologies
title_sort operational characterization of soft topologies by crisp topologies
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-07-01
description 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.
topic soft topology
topology
base for a topology
second-countable space
separability
url https://www.mdpi.com/2227-7390/9/14/1656
work_keys_str_mv AT josecarlosralcantud anoperationalcharacterizationofsofttopologiesbycrisptopologies
AT josecarlosralcantud operationalcharacterizationofsofttopologiesbycrisptopologies
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