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arXiv · 2610.00200

A question of Ulam and a theorem of de Rham

Alexander Lytchak
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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.

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Alexander Lytchak. 2026-09-19. A question of Ulam and a theorem of de Rham. https://arxiv.org/abs/2610.00200

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