Totally bounded ultrametric spaces generated by labeled rays
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917866646798336 |
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| author | Dovgoshey, Oleksiy Vito, Valentino |
| author_facet | Dovgoshey, Oleksiy Vito, Valentino |
| contents | We will say that an infinite tree $T$ is almost a ray if $T$ is the union of a ray and a finite tree. Let $l$ be a non-degenerate labeling of the vertex set $V$ of almost a ray $T$ and let $d_l$ be the corresponding ultrametric on $V$. It is shown that the ultrametric space $(V, d_l)$ is totally bounded iff this space contains an infinite totally bounded subspace. We also prove that the last property characterizes the almost rays. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_15774 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Totally bounded ultrametric spaces generated by labeled rays Dovgoshey, Oleksiy Vito, Valentino General Topology Primary 54E35, Secondary 54E4 We will say that an infinite tree $T$ is almost a ray if $T$ is the union of a ray and a finite tree. Let $l$ be a non-degenerate labeling of the vertex set $V$ of almost a ray $T$ and let $d_l$ be the corresponding ultrametric on $V$. It is shown that the ultrametric space $(V, d_l)$ is totally bounded iff this space contains an infinite totally bounded subspace. We also prove that the last property characterizes the almost rays. |
| title | Totally bounded ultrametric spaces generated by labeled rays |
| topic | General Topology Primary 54E35, Secondary 54E4 |
| url | https://arxiv.org/abs/2402.15774 |