Differences
This shows you the differences between two versions of the page.
| Both sides previous revision Previous revision Next revision | Previous revision Last revision Both sides next revision | ||
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smooth_atlas [2014/12/04 16:40] nikolaj |
smooth_atlas [2014/12/18 18:13] nikolaj |
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| Line 8: | Line 8: | ||
| | @#55EE55: postulate | @#55EE55: $\phi\circ\psi^{-1}$ ... smooth | | | @#55EE55: postulate | @#55EE55: $\phi\circ\psi^{-1}$ ... smooth | | ||
| - | ==== Discussion ==== | ||
| === Formalities === | === Formalities === | ||
| - | "$\phi\circ\psi^{-1}$" in the last line doesn't make sense a priori - their domains/have to be restricted approprietly. | + | 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 $\mathbb R^n$. | ||
