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 homsets are endowed with similar topologies. This paper is devoted to a generalization of classical covering theory in the context of these constructions.
"Semicoverings: a generalization of covering space theory." Homology Homotopy Appl. 14 (1) 33 - 63, 2012.