# Differences

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 smooth_atlas [2014/12/18 18:13]nikolaj smooth_atlas [2014/12/18 18:44] (current)nikolaj Both sides previous revision Previous revision 2014/12/18 18:44 nikolaj 2014/12/18 18:13 nikolaj 2014/12/04 16:42 nikolaj 2014/12/04 16:41 nikolaj 2014/12/04 16:40 nikolaj 2014/12/04 15:57 nikolaj 2014/12/04 15:56 nikolaj 2014/12/04 15:55 nikolaj 2014/12/04 15:55 nikolaj 2014/12/04 15:45 nikolaj 2014/12/04 15:45 nikolaj old revision restored (2014/12/04 14:07) 2014/12/18 18:44 nikolaj 2014/12/18 18:13 nikolaj 2014/12/04 16:42 nikolaj 2014/12/04 16:41 nikolaj 2014/12/04 16:40 nikolaj 2014/12/04 15:57 nikolaj 2014/12/04 15:56 nikolaj 2014/12/04 15:55 nikolaj 2014/12/04 15:55 nikolaj 2014/12/04 15:45 nikolaj 2014/12/04 15:45 nikolaj old revision restored (2014/12/04 14:07) Line 1: Line 1: ===== Smooth atlas ===== ===== Smooth atlas ===== ==== Set ==== ==== Set ==== + | @#55CCEE: context ​    | @#55CCEE: $\langle M,T\rangle$ ... second-countable Hausdorff space | | @#55CCEE: context ​    | @#55CCEE: $\langle M,T\rangle$ ... second-countable Hausdorff space | | @#55CCEE: context ​    | @#55CCEE: $n\in \mathbb N$ | | @#55CCEE: context ​    | @#55CCEE: $n\in \mathbb N$ | Line 8: Line 9: | @#55EE55: postulate ​  | @#55EE55: $\phi\circ\psi^{-1}$ ... smooth | | @#55EE55: postulate ​  | @#55EE55: $\phi\circ\psi^{-1}$ ... smooth | - === Formalities === 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. 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 ==== + === Universal property ​=== + For a smooth atlas there are smooth coordinate changes on $\mathbb R^n$. + + ----- === 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 $\mathbb R^n$. - ==== Parents ==== + ----- === Context* === === Context* === [[Second-countable Hausdorff space]], [[Natural number]] [[Second-countable Hausdorff space]], [[Natural number]]