Homology, Homotopy and Applications

Volume 14 (2012)

Number 1

Semicoverings: a generalization of covering space theory

Pages: 33 – 63

DOI: https://dx.doi.org/10.4310/HHA.2012.v14.n1.a3


Jeremy Brazas (Department of Mathematics and Statistics, Durham, N.H., U.S.A.)


Using universal constructions of topological groups, one can endow the fundamental group of a space with a topology and obtain a topological group. Additionally, the fundamental groupoid of a space becomes enriched over Top when the hom-sets are endowed with similar topologies. This paper is devoted to a generalization of classical covering theory in the context of these constructions.


covering map, groupoid, topological fundamental group, topological group

2010 Mathematics Subject Classification

55Q52, 57M10

Published 13 July 2012