Center of Distances of Ultrametric Spaces Generated by Labeled Trees - UTU Research Portal

A1 Refereed original research article in a scientific journal

Center of Distances of Ultrametric Spaces Generated by Labeled Trees

Authors: Dovgoshey, Oleksiy; Rovenska, Olga

Publisher: MDPI

Publication year: 2026

Journal: Mathematics

Article number: 865

Volume: 14

Issue: 5

eISSN: 2227-7390

DOI: https://doi.org/10.3390/math14050865

Publication's open availability at the time of reporting: Open Access

Publication channel's open availability : Open Access publication channel

Web address : https://doi.org/10.3390/math14050865

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/515683690

Self-archived copy's licence: CC BY

Self-archived copy's version: Publisher`s PDF

Abstract

The center of distances of a metric space (𝑋,𝑑) is the set 𝐶(𝑋) of all 𝑡∈ℝ+ for which the equation 𝑑(𝑥,𝑝)=𝑡 has a solution for each 𝑝∈𝑋. We prove that the equalities 𝐶(𝑋)={0} or 𝐶(𝑋)={0,diam𝑋} hold if (𝑋,𝑑) is an ultrametric space generated by labeled trees. The necessary and sufficient conditions under which diam𝑋∈𝐶(𝑋) are found.

Funding information in the publication:
The first author was supported by grant 367319 of the Research Council of Finland.