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arXiv · 2402.15774

Totally bounded ultrametric spaces generated by labeled rays

Oleksiy Dovgoshey·Valentino Vito
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Abstract

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.

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Oleksiy Dovgoshey, Valentino Vito. 2024-02-24. Totally bounded ultrametric spaces generated by labeled rays. https://arxiv.org/abs/2402.15774

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