Consider the manifold of the real-line R with a differentiable structure generated by the map [tex] x^3 : M \rightarrow \mathbb{R} [/tex]. This example is given in a textbook I'm looking at, but I don't really understand how this can work. The inverse map is clearly not smooth at x=0.(adsbygoogle = window.adsbygoogle || []).push({});

Do they mean that at points like x=0 you have to take different charts, centered at other points besides x^3=0 in the image or something?

(Edited to say smooth instead of continuous.)

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# Example of a differentiable structure on R

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