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 |
| Summary: | 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. |
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| ISSN: | 2075-1680 |