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Nov 8, 2014 at 4:10 comment added LSpice This is quite interesting—but note that Amri's observation on dimension (mathoverflow.net/a/186442/2383) already answers my question as posed, since the dimension of a vector space (even an infinite-dimensional one, if, as here, we are interested only in abstract vector-space isomorphism) determines it up to isomorphism.
Nov 7, 2014 at 13:00 history answered Clément de Seguins Pazzis CC BY-SA 3.0