Konig's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees

Oleksiy Dovgoshey; Olga Rovenska

Konig's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees

General Topology 2026-04-24 v1

Authors: Oleksiy Dovgoshey , Olga Rovenska

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 Konig's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees.

Keywords

ultrametric spaces labeled trees locally finite separable König's Infinity Lemma

Cite

@article{arxiv.2607.14098,
  title  = {Konig's Infinity Lemma for locally finite ultrametric spaces generated by labeled trees},
  author = {Oleksiy Dovgoshey and Olga Rovenska},
  journal= {arXiv preprint arXiv:2607.14098},
  year   = {2026}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2506.03853