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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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Homomorphisms of Topological Groups which are Automatically Fiber Bundles?
The following statement follows from results of Palais (see theorem 2.3.3 in "On the existence of slices for actions of non-compact Lie groups"). When $G$ is a Lie group, any principal $G$-bundle (in …