We prove that Alexander-Spanier cohomology 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.
@article{bwmeta1.element.bwnjournal-article-fmv153i2p154bwm,
author = {Bernd G\"unther and L. Mdzinarishvili},
title = {Continuous Alexander--Spanier cohomology classifies principal bundles with Abelian structure group},
journal = {Fundamenta Mathematicae},
volume = {154},
year = {1997},
pages = {154-156},
zbl = {0891.55004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv153i2p154bwm}
}
Günther, Bernd; Mdzinarishvili, L. Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group. Fundamenta Mathematicae, Tome 154 (1997) pp. 154-156. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv153i2p154bwm/
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