Work

Totally bounded ultrametric spaces generated by labeled rays

Year: 2025

Type: article

Abstract: 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.

Source: Applied General Topology

DOI: 10.4995/agt.2025.21269

Authors: Oleksiy Dovgoshey, Valentino Vito

Institutions: National Academy of Sciences of Ukraine, University of Indonesia

Language: English

Topic: advanced mathematical theories

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Academy of Finland

Award: G348541496