In your statement of Hilbert’s 5th, needn’t we assume G is second-countable? For example, the real line with the discrete topology is locally Euclidean and is not isomorphic to a Lie group.

Thanks.

*[I am not requiring manifolds (or Lie groups) here to be second countable, though one can certainly impose this condition if desired (it doesn’t change the difficulty of Hilbert’s fifth much) -T.]*

Hello, Professor Tao, Louis F. McAuley has published his preprint in arxiv about the proof of Hilbert-Smith conjecture.

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