The pseudometric topology induced by upper asymptotic density
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929533685334016 |
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| author | Keith, Jonathan M. |
| author_facet | Keith, Jonathan M. |
| contents | Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which $P(\mathbb{N})$ is complete. The collection $D$ of sets with asymptotic density is closed in this pseudometric, and closed subsets of $D$ are characterised by a generalisation of an additivity property (AP0). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The pseudometric topology induced by upper asymptotic density Keith, Jonathan M. General Topology Logic 11B05, 54E50 Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which $P(\mathbb{N})$ is complete. The collection $D$ of sets with asymptotic density is closed in this pseudometric, and closed subsets of $D$ are characterised by a generalisation of an additivity property (AP0). |
| title | The pseudometric topology induced by upper asymptotic density |
| topic | General Topology Logic 11B05, 54E50 |
| url | https://arxiv.org/abs/2410.06559 |