%0 Journal Article
%T Topology of the isometry group of the Urysohn space
%A Julien Melleray
%J Mathematics
%D 2009
%I arXiv
%X Using classical results of infinite-dimensional geometry, we show that the isometry group of the Urysohn space, endowed with its usual Polish group topology, is homeomorphic to the separable Hilbert space. The proof is basedon a lemma about extensions of metric spaces by finite metric spaces, which wealso use to investigate (answering a question of I. Goldbring) the relationship, when A,B are finite subsets of the Urysohn space, between the group of isometries fixing A pointwise, the group of isometries fixing B pointwise, and the group of isometries fixing the intersection of A and B pointwise.
%U http://arxiv.org/abs/0907.0413v2