A metric space embedded into a Hilbert space

Question

Suppose $X$ is a metric space but not a Hilbert space, is it possible that it can be isometrically embedded into a Hilbert space? Can anyone give an example?

I don't think so (for an arbitrary metric space) or else the wiki on Kuratowski embedding would say Hilbert space instead of Banach — 3-in-441, Oct 04 '16 at 01:16

score 2 · Answer 1 · answered Oct 04 '16 at 01:05

2

Embed a circle in $R^2$ by the inclusion map.

answered Oct 04 '16 at 01:05

Mark Joshi

5,604

Under what metric? – 89085731 Oct 04 '16 at 01:06
the usual R2 metric – Mark Joshi Oct 04 '16 at 01:12

A metric space embedded into a Hilbert space

1 Answers1