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<p>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 König’s Infinity Lemma for locally finite ultrametric spaces generated by labeled trees.</p>

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Labeled Trees Generating Separable and Locally Finite Ultrametrics

  • 期刊论文

  • 发表日期：

    2026年1月23日

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  • Oleksiy Dovgoshey,
  • Olga Rovenska

摘要

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 König’s Infinity Lemma for locally finite ultrametric spaces generated by labeled trees.