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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Detalles Bibliográficos
Autores: Dovgoshey, Oleksiy, Vito, Valentino
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/221878
Acceso en línea:https://riunet.upv.es/handle/10251/221878
Access Level:acceso abierto
Palabra clave:Cauchy sequence
labeled tree
ray
totally bounded ultrametric space
Descripción
Sumario:[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.