Locally finite ultrametric spaces and labeled trees - UTU Research Portal

A1 Refereed original research article in a scientific journal

Locally finite ultrametric spaces and labeled trees

Authors: Dovgoshey Oleksiy, Kostikov Alexander

Publisher: Springer

Publication year: 2023

Journal: Journal of Mathematical Sciences

Journal name in source: Journal of Mathematical Sciences (United States)

Journal acronym: J. Math. Sci.

Volume: 276

Issue: 5

First page : 614

Last page: 637

eISSN: 1573-8795

DOI: https://doi.org/10.1007/s10958-023-06786-3

Publication's open availability at the time of reporting: No Open Access

Publication channel's open availability : Partially Open Access publication channel

Web address : https://link.springer.com/journal/10958

Preprint address: https://arxiv.org/abs/2308.06626

Abstract

It is shown that a locally finite ultrametric space (X, d) is generated by a labeled tree if and only if for every open ball B ⊆ X there is a point c ∈ B such that d(x, c) = diam B whenever x ∈ B and x ≠ c. For every finite ultrametric space Y, we construct an ultrametric space Z having the smallest possible number of points such that Z is generated by a labeled tree and Y is isometric to a subspace of Z. It is proved that for a given Y such a space Z is unique up to isometry.