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Universal Urysohn space and randomness of the metric spacesColloquium
|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
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.