Compact counterexamples to bi-Lipschitz dimension reduction
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
Scope
The formalized result gives a doubling subset of real $\ell_2$, with doubling constant at most $76800$, that admits no bi-Lipschitz embedding into any finite-dimensional Euclidean space at any finite distortion. A companion gives one universal doubling constant such that every infinite-dimensional real Banach space contains a compact doubling subset with no bi-Lipschitz embedding into any finite-dimensional normed space.
Comparator links
| Result | Comparator statement |
|---|---|
| Doubling Hilbert subset without finite-dimensional embedding | DoublingHilbert.lean |
| Compact counterexamples in infinite-dimensional Banach spaces | CompactBanach.lean |