A1 Refereed original research article in a scientific journal

Totally bounded ultrametric spaces generated by labeled rays



Authors: Dovgoshey, Oleksiy; Vito, Valentino

Publisher: Editorial de la Universidad Politécnica de Valencia

Publication year: 2025

Journal: Applied general topology

Volume: 26

Issue: 1

First page : 163

Last page: 182

ISSN: 1576-9402

eISSN: 1989-4147

DOI: https://doi.org/10.4995/agt.2025.21269

Web address : https://doi.org/10.4995/agt.2025.21269

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/491327663


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 dl be the corresponding ultrametric on V.  It is shown that the ultrametric space (V, dl) is totally bounded if this space contains an infinite totally bounded subspace.  We also prove that the last property characterizes the almost rays.


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Funding information in the publication: 
The first author was supported by grant 359772 of the Academy of Finland.


Last updated on 2025-02-04 at 09:00