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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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Locally compact vs. compactly generated in group theory
I'm studying the Creutz-Shalom paper on the normal subgroup theorem for dense commensurators of lattices. The authors state their results for locally compact and compactly generated groups. I do not h …