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### Universal Urysohn space and randomness of the metric spaces

**Colloquium**

Speaker: | A. Vershik, POMI RAN, Petersburg and MSRI |

Location: | 693 Kerr |

Start time: | Mon, May 20 2002, 4:10PM |

In 1926 P.Urysohn had defined remarkable Universal Metric Space U which is characterized by two properties: 1)each separable metric space can be isometrically imbedded into U, 2)for any two isometrical compact subspaces A and B of U there exist isometry of whole space U which brings A to B. A complete separable space with these two properites is unique upto isometry. Recently becames clear that in some sense a generic separable metric space as well as a random metric space is Urysohn space. There are many links between these facts and random matrices, classification of metrics, Gromov's triples and so on.