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

SIGMA 13 (2017), 098, 10 pages      arXiv:1710.11440      https://doi.org/10.3842/SIGMA.2017.098

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

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

Received December 02, 2017, in final form December 21, 2017; Published online December 31, 2017

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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