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smooth_atlas [2014/12/04 16:41] nikolaj |
smooth_atlas [2014/12/18 18:13] nikolaj |
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| @#55EE55: postulate | @#55EE55: $\phi\circ\psi^{-1}$ ... smooth | | | @#55EE55: postulate | @#55EE55: $\phi\circ\psi^{-1}$ ... smooth | | ||
- | ==== Discussion ==== | ||
=== Formalities === | === Formalities === | ||
- | A priori "$\phi\circ\psi^{-1}$" doesn't make sense as the domain of the functions must be appropriately restricted. | + | A priori "$\phi\circ\psi^{-1}$" in the postulate doesn't make sense as their domains/codomains will not much. Here, really, one must choose functions with appropriately restricted domain. |
+ | ==== Discussion ==== | ||
=== Idea === | === Idea === | ||
For a smooth atlas there are smooth coordinate changes on $\mathbb R^n$. | For a smooth atlas there are smooth coordinate changes on $\mathbb R^n$. |