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.
Homology, Homotopy and Applications, Vol. 14 (2012), No. 1, pp.33-63.
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