The Hilbert–Smith conjecture in every finite dimension
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.
Cite
@misc{OAI:The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026,
author = {{OpenAI}},
title = {{The Hilbert--Smith conjecture in every finite dimension}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026/paper.pdf}{OAI:The-Hilbert-Smith-conjecture-in-every-finite-dimension-September-23-2026}},
year = {2026}
}