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Sep 11, 2013 at 20:12 comment added Tobias Diez Instead of topologicing $Hom(X,Y)$ it is common to resort back to the Gâteaux derivative and see the derivative as a map $df:U \times X \to Y$ instead of $df:U \to Hom(X,Y)$, see ncatlab.org/nlab/show/Fr%C3%A9chet+space#calculus_18
Sep 7, 2013 at 18:17 history answered paul garrett CC BY-SA 3.0