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Oct 3, 2013 at 14:21 comment added Mostafa yes, i asked a new question here: mathoverflow.net/questions/143765/…
Oct 2, 2013 at 0:16 comment added Pietro Majer The question "Is it possible to define a structure of differentiable (smooth) manifold on the Hilbert cube" has a clear meaning to me (is there a differentiable atlas on it compatible with its topology), but maybe you are right, especially reading the OP's comment. In this case the main question would be Andreas Blass': what's a reasonable notion of differentiable maps on the Hilbert cube.
Oct 1, 2013 at 23:21 comment added Igor Belegradek Isn't the OP asking whether one can define differentiable Hilbert cube manifolds, similarly to topological Hilbert cube manifolds? Your answer does not rule this out.
Oct 1, 2013 at 21:46 history answered Pietro Majer CC BY-SA 3.0