On the geometry of Urysohn's universal metric space

DOI10.1016/j.topol.2006.05.005zbMath1113.54017arXivmath/0505508OpenAlexW2088721039MaRDI QIDQ864454

Julien Melleray

Publication date: 9 February 2007

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

Full work available at URL: https://arxiv.org/abs/math/0505508

zbMATH Keywords

isometryPolish groupdefinable equivalence relationUrysohn universal space

Mathematics Subject Classification ID

Complete metric spaces (54E50) Descriptive set theory (03E15) Metric geometry (51F99)

Related Items (24)

An example of a rigid \(\kappa\)-superuniversal metric space ⋮ Completeness of the isomorphism problem for separable \(C^\ast\)-algebras ⋮ Embedding topological fractals in universal spaces ⋮ Extendability of automorphisms of generic substructures ⋮ Functor of extension of contractions on Urysohn universal spaces ⋮ The Katětov construction modified for a \(T_0\)-quasi-metric space ⋮ Topological structure of Urysohn universal spaces ⋮ The conjugacy problem for automorphism groups of countable homogeneous structures ⋮ Growing random graphs with a preferential attachment structure ⋮ On comeager sets of metrics whose ranges are disconnected ⋮ Distances and isomorphism between networks: stability and convergence of network invariants ⋮ Subgroups of isometries of Urysohn-Katětov metric spaces of uncountable density ⋮ Indexability, concentration, and VC theory ⋮ Extending Lipschitz maps into \(C(K)\)-spaces ⋮ Maximal equivariant compactification of the Urysohn spaces and other metric structures ⋮ The oscillation stability problem for the Urysohn sphere: a combinatorial approach ⋮ Some geometric and dynamical properties of the Urysohn space ⋮ On subgroups of minimal topological groups ⋮ Structural Ramsey theory of metric spaces and topological dynamics of isometry groups ⋮ Addendum to ‘The Katětov construction modified for a T₀-quasi-metric space’ ⋮ Ultra-\(\mathfrak m\)-separability ⋮ Isometric embeddings of Polish ultrametric spaces ⋮ When separability of the space of ultra-extremal functions is preserved ⋮ Polish groupoids and functorial complexity

Cites Work

• The Urysohn universal metric space is homeomorphic to a Hilbert space
• Some isometry groups of the Urysohn space
• The universal Urysohn space, Gromov metric triples and random metrics on the natural numbers
• On the classification of Polish metric spaces up to isometry
• Extension of compact operators
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