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

DOI10.1016/j.topol.2021.107759zbMath1472.51007arXiv2007.08105OpenAlexW3177036535MaRDI QIDQ2049876

Zhengchao Wan

Publication date: 27 August 2021

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.08105

zbMATH Keywords

dendrogramsGromov-Hausdorff ultrametricuniversal ultrametric space

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Metric geometry (51F99)

Related Items (7)

An embedding, an extension, and an interpolation of ultrametrics ⋮ On \(p\)-metric spaces and the \(p\)-Gromov-Hausdorff distance ⋮ Branching geodesics of the Gromov-Hausdorff distance ⋮ Constructions of Urysohn universal ultrametric spaces ⋮ The ultrametric Gromov-Wasserstein distance ⋮ Uniqueness and homogeneity of non-separable Urysohn universal ultrametric spaces ⋮ On comeager sets of metrics whose ranges are disconnected

Cites Work

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• Polish ultrametric Urysohn spaces and their isometry groups
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Geometry of non-Archimedean Gromov-Hausdorff distance
• The Gromov-Hausdorff hyperspace of a Euclidean space
• Local structure of Gromov-Hausdorff space, and isometric embeddings of finite metric spaces into this space
• On the universal ultrametric space
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

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