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arXiv · 2007.08105

A novel construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric

Zhengchao Wan
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Abstract

We establish universality and ultra-homogeneity of $(\mathcal{U},u_\mathrm{GH})$, the collection of all compact ultrametric spaces endowed with the so-called Gromov-Hausdorff ultrametric. This result also gives rise to a novel construction of the so-called $R$-Uryoshn universal ultrametric space for each countable subset $R\subset\mathbb{R}_{\geq 0}$ containing $0$.

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Zhengchao Wan. 2020-07-16. A novel construction of Urysohn universal ultrametric space via the Gromov-Hausdorff ultrametric. https://arxiv.org/abs/2007.08105

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