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Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group

Bernd GüntherL. Mdzinarishvili — 1997

Fundamenta Mathematicae

We prove that Alexander-Spanier cohomology H n ( X ; G ) with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.

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