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# Uniform Embeddings into Hilbert Space and a Question of Gromov

Published:2002-03-01
Printed: Mar 2002
• A. N. Dranishnikov
• G. Gong
• V. Lafforgue
• G. Yu
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## Abstract

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.
 MSC Classifications: 46C05 - Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)