2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74259Answering 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.Metric GeometryGroup Theory51F99; 22A05text