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for questions about fiber bundles, including structure groups, principal bundles, and spaces of sections.
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Why is any $G$-resolution a principal $G$-bundle?
In the article The Cohomology of Classifying Spaces of H-Spaces by M. Rothenberg and N. Steenrod (https://projecteuclid.org/euclid.bams/1183527356) it is stated as a theorem that if $G$ is a topologic …