Stabilizers of closed sets in the Urysohn space

• Autorzy: Julien Melleray
• Języki publikacji: EN

Abstrakty

EN

Building on earlier work of Katětov, Uspenskij proved in [8] that the group of isometries of Urysohn's universal metric space 𝕌, endowed with the pointwise convergence topology, is a universal Polish group (i.e. it contains an isomorphic copy of any Polish group). Answering a question of Gao and Kechris, we prove here the following, more precise result: for any Polish group G, there exists a closed subset F of 𝕌 such that G is topologically isomorphic to the group of isometries of 𝕌 which map F onto itself.

Kategorie tematyczne

• 22F50: Groups as automorphisms of other structures
• 51F99: None of the above, but in this section
• 22A05: Structure of general topological groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 1
• Strony: 53-60

Daty

wydano

2006

Twórcy

autor

Julien Melleray

• Équipe d'Analyse Fonctionnelle, Université Paris 6, Boîte 186, 4 Place Jussieu, 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/fm189-1-4