Vladimir Uspenskij
Published 2003-09-05Version 1
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).
All $\mathbb Q$-gluons are homeomorphic
Characterizing Lipschitz images of injective metric spaces
The unit ball of the Hilbert space in its weak topology
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