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arXiv · 2506.03853

Labeled Trees Generating Separable and Locally Finite Ultrametrics

Oleksiy Dovgoshey·Olga Rovenska
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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.

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Oleksiy Dovgoshey, Olga Rovenska. 2025-06-04. Labeled Trees Generating Separable and Locally Finite Ultrametrics. https://arxiv.org/abs/2506.03853

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