### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 070, 11 pages      arXiv:1805.03066      https://doi.org/10.3842/SIGMA.2018.070

### The Solution of Hilbert's Fifth Problem for Transitive Groupoids

Paweł Raźny
Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University in Cracow, Poland

Received May 11, 2018, in final form July 10, 2018; Published online July 17, 2018

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 the 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.

Key words: Lie groupoids; topological groupoids.

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