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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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On the group of isometries of the Urysohn universal metric space
by
Vladimir Uspenskiy
Ohio University, USA

The Urysohn universal metric space U is characterized by the following properties: U is a complete separable metric space, U contains an isometric copy of any other separable metric space, and any isometry between finite subspaces of U extends to an isometry of U onto itself. The topological group Is(U) of all isometries of U is a universal topological group with a countable base. This group has interesting properties, for example, it is extremely amenable (Pestov). It follows that Is(U) is not isomorphic to another universal topological group with a countable base, the group of all self-homeomorphisms of the Hilbert cube.

Date received: June 25, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-62.