Stabilizers of closed sets in the Urysohn space

Julien Melleray. "Stabilizers of closed sets in the Urysohn space." Fundamenta Mathematicae 189.1 (2006): 53-60. <http://eudml.org/doc/282707>.

@article{JulienMelleray2006,
abstract = {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.},
author = {Julien Melleray},
journal = {Fundamenta Mathematicae},
keywords = {Urysohn space; Polish group; isometry group; Katětov map},
language = {eng},
number = {1},
pages = {53-60},
title = {Stabilizers of closed sets in the Urysohn space},
url = {http://eudml.org/doc/282707},
volume = {189},
year = {2006},
}

TY - JOUR
AU - Julien Melleray
TI - Stabilizers of closed sets in the Urysohn space
JO - Fundamenta Mathematicae
PY - 2006
VL - 189
IS - 1
SP - 53
EP - 60
AB - 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.
LA - eng
KW - Urysohn space; Polish group; isometry group; Katětov map
UR - http://eudml.org/doc/282707
ER -