The Seifert and Van Kampen
theorem has lately been phrased as the solution to a universal mapping problem.
There is given here an analogous theorem for regular covering spaces, regarded as
principal bundles with discrete structure groups. The universal covering space of a
union of two spaces is built up from the universal covering spaces of the two
subspaces by an application of the associated bundle and clutching constructions.
When all spaces are semi-locally simply connected, the Seifert and Van Kampen
theorem is a consequence.