Stabilizers of closed sets in the Urysohn space

Mathematics – Metric Geometry

Scientific paper

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Scientific paper

Answering a question of Gao and Kechris, we show that, given any polish group
G, there exists a closed subset F of Urysohn's universal metric space U such
that G is (topologically) isomorphic to the subgroup of isometries of U which
map F onto itself.

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