Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space

DOI10.1016/j.topol.2008.03.007zbMath1160.54020arXiv0803.4300OpenAlexW2963388700MaRDI QIDQ935263

Anatoly M. Vershik

Publication date: 6 August 2008

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

Full work available at URL: https://arxiv.org/abs/0803.4300

zbMATH Keywords

isometry groupUrysohn metric spaceextension of partial isometries

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Metric spaces, metrizability (54E35) Topological groups (topological aspects) (54H11) Groups as automorphisms of other structures (22F50)

Related Items (18)

All those EPPA classes (strengthenings of the Herwig–Lascar theorem) ⋮ Completing graphs to metric spaces ⋮ On subgroups of minimal topological groups ⋮ Dense locally finite subgroups of automorphism groups of ultraextensive spaces ⋮ Ramsey properties and extending partial automorphisms forhbox classes of finite structures ⋮ Structural Ramsey theory of metric spaces and topological dynamics of isometry groups ⋮ Uncountable graphs and invariant measures on the set of universal countable graphs ⋮ Extending partial isometries of antipodal graphs ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ Homogeneous spaces with inner metric and with integrable invariant distributions ⋮ The Hrushovski property for hypertournaments and profinite topologies ⋮ EPPA for two-graphs and antipodal metric spaces ⋮ A combinatorial proof of the extension property for partial isometries ⋮ Conant's generalised metric spaces are Ramsey ⋮ Nonpositive curvature is not coarsely universal ⋮ Isometry groups of Borel randomizations ⋮ Unnamed Item ⋮ Extension of isometries in real Hilbert spaces

Cites Work

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• The isometry group of the Urysohn space as a Lévy group
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• Homogeneous Cayley objects
• Classification of measurable functions of several variables and invariantly distributed random matrices
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• Extending partial isomorphisms on finite structures
• Ubiquity in category for metric spaces and transition systems
• Extending partial isometries
• Some isometry groups of the Urysohn space
• The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers
• Extending partial automorphisms and the profinite topology on free groups
• Linearly rigid metric spaces and the embedding problem
• 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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