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

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.

arXiv admin note: substantial text overlap with arXiv:2506.03853