Year: 2026
Type: preprint
Abstract: We generalize de Rham's decomposition theorem to proper metric spaces: every proper metric space has a unique decomposition as the product of a Euclidean space and a finite or countable pointed $\ell^2$-product of nontrivial irreducible non-Euclidean factors. More generally, every complete metric space splits canonically into a Hilbert factor, a pointed $\ell^2$-product of irreducible non-Euclidean factors, and a factor with no nontrivial irreducible factors. These results partially answer a question of Ulam.
Source: arXiv (Cornell University)
Author: Lytchak, Alexander
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W7215842671