  The Urysohn universal metric space U is characterized up to isometry by the
following properties: (1) U is complete and separable; (2) U contains an
isometric copy of every separable metric space; (3) every isometry between two
finite subsets of U can be extended to an isometry of U onto itself. We show
that U is homeomorphic to the Hilbert space l_2 (or to the countable power of
the real line).
