Timeline for Embedding a countably infinite metric space in $\ell^2(\mathbb Z_+)$
Current License: CC BY-SA 4.0
7 events
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| Feb 5 at 23:18 | comment | added | YCor | Alternatively, it follows from a standard ultraproduct procedure (using that the metric ultraproduct of Hilbert spaces is Hilbert). But of course this is essentially a nonstandard restatement of Christian Remling's answer. | |
| Feb 5 at 23:15 | comment | added | YCor | It's true ($X$ need not be finite if you allow arbitrary Hilbert spaces). A (semi)metric space is isometrically embeddable into a Hilbert space iff the square of its distance is conditionally negative definite, and the latter condition is finitary. | |
| Feb 5 at 18:42 | answer | added | Christian Remling | timeline score: 3 | |
| Feb 5 at 18:29 | history | edited | Daniel Asimov | CC BY-SA 4.0 |
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| Feb 5 at 18:27 | history | edited | Christian Remling | CC BY-SA 4.0 |
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| Feb 5 at 18:23 | history | edited | Michael Hardy | CC BY-SA 4.0 |
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| Feb 5 at 18:04 | history | asked | Daniel Asimov | CC BY-SA 4.0 |