The linear isometry group of the Gurarij space is universal

DOI10.1090/S0002-9939-2014-11956-3zbMath1311.46004arXiv1203.4915OpenAlexW1979541375MaRDI QIDQ5418555

Itaï Ben Yaacov

Publication date: 4 June 2014

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1203.4915

zbMATH Keywords

Arens-Eells spaceGurarij spaceKatetov functionslinear isometry groupuniversal Polish group

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Topological groups (topological aspects) (54H11) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Isometric theory of Banach spaces (46B04)

Related Items (23)

Metrical universality for groups ⋮ Uniqueness, universality, and homogeneity of the noncommutative Gurarij space ⋮ An example of a non-commutative uniform Banach group ⋮ On a Roelcke-precompact Polish group that cannot act transitively on a complete metric space ⋮ A topological transformation group without non-trivial equivariant compactifications ⋮ Metric Scott analysis ⋮ Katětov functors ⋮ Retracts of ultrahomogeneous structures in the context of Katětov functors ⋮ Approximate isomorphism of metric structures ⋮ Homotopy and universality ⋮ Maximal equivariant compactifications ⋮ (Isometric) universality and actions of spaces, continuously containing topological groups ⋮ Unnamed Item ⋮ Maximal equivariant compactification of the Urysohn spaces and other metric structures ⋮ Non-universality of automorphism groups of uncountable ultrahomogeneous structures ⋮ On actions of spaces continuously containing topological groups ⋮ Polish groups and Baire category methods ⋮ Fraïssé and Ramsey properties of Fréchet spaces ⋮ Fraïssé limits in functional analysis ⋮ On spaces continuously containing topological groups ⋮ Projectively universal countable metrizable groups ⋮ Generic representations of countable groups ⋮ A rigid Urysohn-like metric space

Cites Work

• A proof of uniqueness of the Gurariĭ space
• On subgroups of minimal topological groups
• The Gurarij spaces are unique
• Generic orbits and type isolation in the Gurarij space
• FRAÏSSÉ LIMITS OF METRIC STRUCTURES
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