A subset of real Hilbert space has doubling constant at most 76,800 yet admits no bi-Lipschitz embedding into any finite-dimensional Euclidean space at any finite distortion.
A subset of real Hilbert space has doubling constant at most 76,800 yet admits no bi-Lipschitz embedding into any finite-dimensional Euclidean space at any finite distortion. Moreover, every infinite-dimensional real Banach space contains a compact doubling subset with the analogous obstruction and a universal doubling bound.
A subset of real Hilbert space has doubling constant at most 76,800 yet admits no bi-Lipschitz embedding into any finite-dimensional Euclidean space at any finite distortion. Moreover, every infinite-dimensional real Banach space contains a compact doubling subset with the analogous obstruction and a universal doubling bound.
If correct, answers the Lang–Plaut dimension-reduction question negatively even in Hilbert space and extends the obstruction to all infinite-dimensional real Banach spaces.
Must every doubling subset of Hilbert space embed bi-Lipschitzly in some finite-dimensional Euclidean space?
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OpenAI reports a doubling Hilbert set with no finite-dimensional bi-Lipschitz embedding
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