Labeled Trees Generating Separable and Locally Finite Ultrametrics
General Topology
2025-06-10 v2
Abstract
We analyze the interplay between labeled trees and the ultrametric spaces they present. We provide characterizations of labeled trees that generate separable ultrametric spaces and those that generate locally finite ultrametric spaces. In particular, we establish an analog of K\"onig's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees.
Keywords
Cite
@article{arxiv.2506.03853,
title = {Labeled Trees Generating Separable and Locally Finite Ultrametrics},
author = {Oleksiy Dovgoshey and Olga Rovenska},
journal= {arXiv preprint arXiv:2506.03853},
year = {2025}
}