Vol. 49, No. 1, 1973

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The Seifert and Van Kampen theorem via regular covering spaces

R. J. Knill

Vol. 49 (1973), No. 1, 149–160

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.

Mathematical Subject Classification
Primary: 55A10
Received: 23 June 1972
Revised: 15 May 1973
Published: 1 November 1973
R. J. Knill