The Hilbert–Smith conjecture in every dimension at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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The Hilbert–Smith conjecture in every dimension

at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Difficulty:	🧠🧠🧠🧠🧠	Ages:	13 - ∞
Skills:	donuts, coffee cups	Levels:	1
Category:	Topology	Lean version:	not yet
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The Hilbert–Smith conjecture in every dimension. Every locally compact second-countable Hausdorff group acting faithfully and jointly continuously on a connected finite-dimensional topological manifold is a Lie group. This proves the Hilbert–Smith conjecture in all finite dimensions, for Hausdorff second-countable manifolds without boundary.

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LEVEL 1 The Hilbert–Smith conjecture in every finite dimension

released 2026-09-23 | 9 theorems · 16 lemmas · 40 proofs · 21,279 words | PLAY LEVEL 1 » (pdf)

We prove the Hilbert–Smith conjecture in every finite dimension: every locally compact second-countable Hausdorff group acting faithfully and jointly continuously on a connected Hausdorff second-countable finite-dimensional topological manifold without boundary is a Lie group.

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