Hilbert–Smith conjecture

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In mathematics, the Hilbert–Smith conjecture is concerned with the possible transformation groups of manifolds. The conjecture says that if a locally compact topological group G act faithfully and continuous on a connected manifold M, then G must be a Lie group. The naming of the conjecture is for David Hilbert, and Paul A. Smith. It is considered by some to be a better formulation of Hilbert's fifth problem, than the characterisation of topological groups being also a topological manifolds as Lie groups often cited as a solution.

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