Geodesic
Stabilizers of closed sets in the Urysohn space
Julien Melleray1
1 Équipe d'Analyse Fonctionnelle Université Paris 6 Boîte 186, 4 Place Jussieu 75252 Paris Cedex 05, France
Fundamenta Mathematicae, Tome 189 (2006) no. 1, pp. 53-60.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Building on earlier work of Katětov, Uspenskij proved in \cite{Uspenskij2} that the group of isometries of Urysohn's universal metric space $\mathbb 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 $\mathbb U$ such that $G$ is topologically isomorphic to the group of isometries of $\mathbb U$ which map $F$ onto itself.
DOI : 10.4064/fm189-1-4
Keywords: building earlier work kat tov uspenskij proved cite uspenskij group isometries urysohns universal metric space mathbb endowed pointwise convergence topology universal polish group contains isomorphic copy polish group answering question gao kechris prove here following precise result polish group there exists closed subset mathbb topologically isomorphic group isometries mathbb which map itself

Julien Melleray 1

1 Équipe d'Analyse Fonctionnelle Université Paris 6 Boîte 186, 4 Place Jussieu 75252 Paris Cedex 05, France 
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Julien Melleray. Stabilizers of closed sets in the Urysohn space. Fundamenta Mathematicae, Tome 189 (2006) no. 1, pp. 53-60. doi : 10.4064/fm189-1-4. http://geodesic.mathdoc.fr/articles/10.4064/fm189-1-4/

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