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SUMMARY:Ultrametric subsets with large Hausdorff dimension - Mendel\, M (O
 pen University of Israel)
DTSTART:20110111T113000Z
DTEND:20110111T123000Z
UID:TALK28835@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We show that for any 1>ε>0\, any metric space X contains a su
 bset Y which is O(1/ε) equivalent to an ultrametric and dimH(Y)>(1-ε)dim
 H(X)\, where dimH is the Hausdorff dimension. The dependence on ε is tigh
 t up-to a constant multiplicative factor. \n\nThis result can be viewed as
  high distortion metric analog of Dvoretzky theorem. Low distortion analog
  of Dvoretzky theorem is impossible since there are examples of compact me
 tric spaces of arbitrary large Hausdorff dimension for which any subset th
 at embeds in Hilbert space with distortion smaller than 2 must have zero H
 ausdorff dimension. \n
LOCATION:Seminar Room 1\, Newton Institute
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