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smooth_atlas [2014/12/18 18:13]
nikolaj
smooth_atlas [2014/12/18 18:44] (current)
nikolaj
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 ===== 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: $n\in \mathbb N$ |
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 | @#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]]
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