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Dec 4, 2016 at 7:44 comment added YCor Note that I didn't answer the question about closedness of the adjoint representation. This post only shows that it has closed image when $G/Z(G)$ has compact abelianization, and this is not optimal (e.g., when $G$ is algebraic it also has a closed image).
Oct 5, 2014 at 1:10 comment added Selene Routley Very slick indeed. Most wonderful. Many thanks, Yves
Oct 5, 2014 at 1:10 vote accept Selene Routley
Oct 4, 2014 at 12:58 history answered YCor CC BY-SA 3.0