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Totally bounded ultrametric spaces generated by labeled rays

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arxiv 2402.15774 v2 pith:XHC5ICTA submitted 2024-02-24 math.GN

Oleksiy Dovgoshey , Valentino Vito This is my paper · ORCID
classification math.GN
keywords almostboundedtotallyultrametricinfiniteraysspacetree
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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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  1. Ultrametric spaces generated by labeled star graphs

    math.GN 2025-02 conditional novelty 6.0 of 10

    An ultrametric space comes from a labeled star graph exactly when some point is no farther from any point than that point is from every other point, and its self-isometries match the graph's symmetries exactly when th...

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