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

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 $R\subset {\mathbb{R}}_{\ge 0}$ containing $0$.

11 pages