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Uniform Embeddings into Hilbert Space and a Question of Gromov

Published online by Cambridge University Press:  20 November 2018

A. N. Dranishnikov ,
G. Gong ,
V. Lafforgue  and
G. Yu
A. N. Dranishnikov
Affiliation:
Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA, email: dranish@math.psu.edu
G. Gong
Affiliation:
Department of Mathematics, University of Puerto Rico, Rio Piedras, San Juan, PR 00931 USA, email: ggong@upracd.upr.clu.edu
V. Lafforgue
Affiliation:
Laboratoire de Mathématiques de l’Ecole Normale Supérieure, 45 rue d’Ulm, 75230 Paris Cedex 05, France, email: vlafforg@dmi.ens.fr
G. Yu
Affiliation:
Department of Mathematics, University of Colorado, Boulder, CO 80309–0395, USA, email: gyu@euclid.colorado.edu
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Abstract

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Gromov introduced the concept of uniform embedding into Hilbert space and asked if every separable metric space admits a uniform embedding into Hilbert space. In this paper, we study uniform embedding into Hilbert space and answer Gromov’s question negatively.

Keywords

46C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 60 - 70
Copyright
Copyright © Canadian Mathematical Society 2002

References

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