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International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 3, Pages 131-140

Extendibility, monodromy, and local triviality for topological groupoids

1Department of Mathematics, Faculty of Science and Art, Erciyes University, Kayseri, Turkey
2Department of Mathematics, Faculty of Science and Art, İnönü University, Malatya, Turkey

Received 11 September 2000; Revised 26 February 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A groupoid is a small category in which each morphism has an inverse. A topological groupoid is a groupoid in which both sets of objects and morphisms have topologies such that all maps of groupoid structure are continuous. The notion of monodromy groupoid of a topological groupoid generalizes those of fundamental groupoid and universal cover. It was earlier proved that the monodromy groupoid of a locally sectionable topological groupoid has the structure of a topological groupoid satisfying some properties. In this paper a similar problem is studied for compatible locally trivial topological groupoids.