Sequences suffice for pointfree uniform completions
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908559462105088 |
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| author | Manuell, Graham |
| author_facet | Manuell, Graham |
| contents | Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15569 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sequences suffice for pointfree uniform completions Manuell, Graham General Topology 06D22, 54E15, 54A20, 54D35 Completions of metric spaces are usually constructed using Cauchy sequences. However, this does not work for general uniform spaces, where Cauchy filters or nets must be used instead. The situation in pointfree topology is more straightforward: the correct completion of uniform locales can indeed be obtained as a quotient of a locale of Cauchy sequences. |
| title | Sequences suffice for pointfree uniform completions |
| topic | General Topology 06D22, 54E15, 54A20, 54D35 |
| url | https://arxiv.org/abs/2409.15569 |