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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| Format: | Article |
| Language: | English |
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/14/1656 |
| _version_ | 1827687377744691200 |
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| author | José Carlos R. Alcantud |
| author_facet | José Carlos R. Alcantud |
| author_sort | José Carlos R. Alcantud |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T09:32:36Z |
| format | Article |
| id | doaj.art-a28aa4f250de4a4da2a437c517ba86a4 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:32:36Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a28aa4f250de4a4da2a437c517ba86a42023-11-22T04:20:11ZengMDPI AGMathematics2227-73902021-07-01914165610.3390/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 |
| 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 |
| title | 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_short | An Operational Characterization of Soft Topologies by Crisp Topologies |
| title_sort | operational characterization of soft topologies by crisp topologies |
| 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 |