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In the following paper we investigate the question: when is a transitivetopological groupoid continuously isomorphic to a Lie groupoid? We present manyresults on the matter which may be considered generalizations of the Hilbert'sfifth problem to this context. Most notably we present a "solution" to theproblem for proper transitive groupoids and transitive groupoids with compactsource fibers.

On the Generalization of Hilbert's Fifth Problem to Transitive Groupoids