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Dec 24, 2012 at 6:30 vote accept Leonard
Dec 19, 2012 at 19:06 history edited Peter Michor CC BY-SA 3.0
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Dec 19, 2012 at 18:17 comment added Todd Trimble If the nLab gives a correct reference, then Boman proved it in 1967. Reference: Jan Boman, Differentiability of a function and of its compositions with functions of one variable, Math. Scand. 20 1967 249–268.
Dec 19, 2012 at 10:11 history edited Peter Michor CC BY-SA 3.0
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Dec 19, 2012 at 3:47 comment added Paul Siegel I can't believe the result is really that recent: I've seen a version of (2) as a definition of smoothness in old differential geometry books. Aside from that, I remember this being assigned as a homework problem in an analysis class; it's harder than it seems at first, but it just came down to compactness of the circle if I recall correctly.
Dec 19, 2012 at 2:13 comment added Leonard Very interesting indeed! Looks trivial, but after looking at the actual proof, I am deeply impressed by its depth.
Dec 18, 2012 at 21:30 comment added Todd Trimble Wow! That's interesting.
Dec 18, 2012 at 19:09 history answered Peter Michor CC BY-SA 3.0