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Feb 22, 2013 at 15:27 comment added Gerald Edgar A nice example. But again in this case, the isomorphism as groups requires AC for proof.
Oct 30, 2010 at 15:49 comment added Bill Johnson Kadec proved that all separable infinite dimensional Banach spaces are homeomorphic and all are clearly isomorphic to one another but as topological groups there are a continuum of different ones.
Oct 30, 2010 at 5:46 history answered Ady CC BY-SA 2.5