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A topological group is a group $G$ together with a topology on the elements of $G$ such that the group operation and group inverse function are both continuous (with respect to the topology).

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Principal bundles from a fibration of homogeneous spaces

I call such bundles "homogeneous bundles", but it's not a totally standard terminology. It is true that the map $G/H\rightarrow G/H'$ is a fiber bundle map with fiber $H/H'$. One way to see this is t …
Jason DeVito - on hiatus's user avatar