Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group
Volume 153 / 1997
Fundamenta Mathematicae 153 (1997), 154-156
DOI: 10.4064/fm-153-2-154-156
Abstract
We prove that Alexander-Spanier cohomology $H^n(X;G)$ with coefficients in a topological} Abelian 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.
