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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.
Sur un espace métrique universel
P. Urysohn · 1927
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Groups of polynomial growth and expanding maps
M. Gromov · 1981
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On the universal ultrametric space
I.A. Vestfrid · 1994
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I. Zarichnyi · 2005
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Metric structures for Riemannian and non-Riemannian spaces
M. Gromov · 2007
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Geometry of non-archimedean Gromov-Hausdorff distance
D. Qiu · 2009
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Characterization, stability and convergence of hierarchical clustering methods
G. Carlsson and F. Mémoli · 2010
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Polish ultrametric Urysohn spaces and their isometry groups
S. Gao and C. Shao · 2011
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Local structure of Gromov-Hausdorff space, and isometric embeddings of finite metric spaces into this space
S. Iliadis, A.O. Ivanov, and A.A. Tuzhilin · 2017
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F. Mémoli, Z. Smith, and Z. Wan · 2019
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The Gromov-Hausdorff hyperspace of a Euclidean space
S.A. Antonyan · 2020
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