Stabilizers of closed sets in the Urysohn space
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.
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
Affiliations des auteurs :
Julien Melleray 1
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author = {Julien Melleray},
title = {Stabilizers of closed sets in the {Urysohn} space},
journal = {Fundamenta Mathematicae},
pages = {53--60},
publisher = {mathdoc},
volume = {189},
number = {1},
year = {2006},
doi = {10.4064/fm189-1-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm189-1-4/}
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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
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