Homology, Homotopy and Applications
Volume 14 (2012)
Semicoverings: a generalization of covering space theory
Pages: 33 – 63
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