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 show english descriptions Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 46C05 - Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

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