Center of distances of ultrametric spaces generated by labeled trees

2026/01/19 by Oleksiy Dovgoshey, Olga Rovenska · 1 voice · 1 citation
Mathematics · #math.GN

paper · pdf · doi:10.3390/math14050865

arxiv published 2026/01/19 · arxiv updated 2026/02/20

Abstract

The center of distances of a metric space (X,d) is the set C(X) of all t∈ \mathbb R⁺ for which the equation d(x,p)=t has a solution for each p∈ X. We prove that the equalities C(X)=\0\ or C(X)=\0,diamX\ hold if (X,d) is an ultrametric space generated by labeled trees. The necessary and sufficient conditions under which diam X∈ C(X) are found.

Citations

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• Finite Ultrametric Balls
• On generating regular Cantorvals connected with geometric Cantor sets
• On the center of distances
• Encyclopedia of Distances
• Weak similarities of metric and semimetric spaces
• Diameter and diametrical pairs of points in ultrametric spaces
• Indivisible ultrametric spaces

Cited by

• The Gomory-Hu inequality and trees

Discussions

• Oleksiy Dovgoshey, Olga Rovenska: Center of distances of ultrametric spaces generated by labeled trees https://arxiv.org/abs/2601.13363 https://arxiv.org/pdf/2601.13363 https://arxiv.org/html/2601.133 [bsky, 0 points, 0 comments]

Related

• Locally finite ultrametric spaces and labeled trees
• Labeled trees generating complete, compact, and discrete ultrametric spaces
• Labeled Trees Generating Separable and Locally Finite Ultrametrics
• The Gomory-Hu inequality and trees
• Longest paths in trees and isometricity of ultrametric spaces