Semicoverings: a generalization of covering space theory

TL;DR

This paper generalizes classical covering space theory by enriching the fundamental groupoid with topological structures related to topological groups, broadening the scope of covering space concepts.

Contribution

It introduces a new framework that extends covering space theory using topological group structures on the fundamental groupoid.

Findings

Enriched fundamental groupoid with topological structures

Generalization of classical covering theory

Connections to universal constructions of topological groups

Abstract

The fundamental groupoid of a space becomes enriched over the category of topological spaces when the hom-sets are endowed with topologies intimately related to universal constructions of topological groups. This paper is devoted to a generalization of classical covering theory in the context of this construction.