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Totally bounded ultrametric spaces generated by labeled rays

  • Dovgoshey, Oleksiy [1] ; Vito, Valentino [2]
    1. [1] National Academy of Sciences of Ukraine

      National Academy of Sciences of Ukraine

      Ucrania

    2. [2] University of Indonesia

      University of Indonesia

      Indonesia

  • Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 1, 2025, págs. 163-182
  • Idioma: inglés
  • DOI: 10.4995/agt.2025.21269
  • Enlaces
  • Resumen

    • 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.

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