Investigation of Proximal Spaces Using Relators
In this paper, we define uniformities and proximities as relators and show the equivalences of these definitions with classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz. Moreover, we prove implications between important topol...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/10/3/143 |
| _version_ | 1797528205672841216 |
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| author | Gergely Pataki |
| author_facet | Gergely Pataki |
| author_sort | Gergely Pataki |
| collection | DOAJ |
| description | In this paper, we define uniformities and proximities as relators and show the equivalences of these definitions with classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz. Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we add an analogous definition for uniformly and proximally filtered properties. |
| first_indexed | 2024-03-10T09:54:51Z |
| format | Article |
| id | doaj.art-84810cf4127c47b3a21072a18e7d7f22 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T09:54:51Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-84810cf4127c47b3a21072a18e7d7f222023-11-22T02:27:17ZengMDPI AGAxioms2075-16802021-06-0110314310.3390/axioms10030143Investigation of Proximal Spaces Using RelatorsGergely Pataki0Department of Mathematical Analysis, Budapest University of Technology and Economics, H1111 Budapest, HungaryIn this paper, we define uniformities and proximities as relators and show the equivalences of these definitions with classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz. Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we add an analogous definition for uniformly and proximally filtered properties.https://www.mdpi.com/2075-1680/10/3/143(generalized) uniformities(generalized) proximitiesrelators |
| spellingShingle | Gergely Pataki Investigation of Proximal Spaces Using Relators Axioms (generalized) uniformities (generalized) proximities relators |
| title | Investigation of Proximal Spaces Using Relators |
| title_full | Investigation of Proximal Spaces Using Relators |
| title_fullStr | Investigation of Proximal Spaces Using Relators |
| title_full_unstemmed | Investigation of Proximal Spaces Using Relators |
| title_short | Investigation of Proximal Spaces Using Relators |
| title_sort | investigation of proximal spaces using relators |
| topic | (generalized) uniformities (generalized) proximities relators |
| url | https://www.mdpi.com/2075-1680/10/3/143 |
| work_keys_str_mv | AT gergelypataki investigationofproximalspacesusingrelators |