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arXiv · 2601.13363

Center of distances of ultrametric spaces generated by labeled trees

Oleksiy Dovgoshey·Olga Rovenska
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Abstract

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

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Oleksiy Dovgoshey, Olga Rovenska. 2026-01-19. Center of distances of ultrametric spaces generated by labeled trees. https://arxiv.org/abs/2601.13363

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