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

Volume 153 / 1997

R. Günter, L. Mdzinarishvili Fundamenta Mathematicae 153 (1997), 154-156 DOI: 10.4064/fm-153-2-154-156


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.


  • R. Günter
  • L. Mdzinarishvili

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