Vol. 37, No. 1, 1971

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On covering spaces and Galois extensions

Lindsay Nathan Childs

Vol. 37 (1971), No. 1, 29–33

Let X be a connected compact Hausdorff space, and G a finite abelian group. In this note we obtain a short exact sequence (Theorem 1) which describes the group of isomorphism classes of regular covering spaces of X with group G. The sequence is derived as an immediate translation of a similar sequence involving the group of commutative Galois extensions with group G of C(X), the ring of complex-valued continuous functions on X.

Mathematical Subject Classification 2000
Primary: 54C40
Secondary: 16A74
Received: 19 February 1970
Published: 1 April 1971
Lindsay Nathan Childs