The Solution of Hilbert's Fifth Problem for Transitive Groupoids

Abstract

In the following paper, we investigate the question: when is a transitive topological groupoid continuously isomorphic to a Lie groupoid? We present many results on the matter, which may be considered generalizations of Hilbert's fifth problem to this context. Most notably, we present a "solution" to the problem for proper transitive groupoids and transitive groupoids with compact source fibers.