Totally bounded ultrametric spaces generated by labeled rays

[EN] We will say that a 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 dI be the corresponding ultrametric on V. It is shown that the ultrametric space (V, dI ) is totally bounded iff this space co...

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Bibliographic Details
Authors: Dovgoshey, Oleksiy, Vito, Valentino
Format: article
Publication Date:2025
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/221878
Online Access:https://riunet.upv.es/handle/10251/221878
Access Level:Open access
Keyword:Cauchy sequence
labeled tree
ray
totally bounded ultrametric space
Description
Summary:[EN] We will say that a 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 dI be the corresponding ultrametric on V. It is shown that the ultrametric space (V, dI ) is totally bounded iff this space contains an infinite totally bounded subspace. We also prove that the last property characterizes the almost rays.