===== Smooth atlas =====
==== Set ====

| @#55CCEE: context     | @#55CCEE: $\langle M,T\rangle$ ... second-countable Hausdorff space |
| @#55CCEE: context     | @#55CCEE: $n\in \mathbb N$ |
| @#FFBB00: definiendum | @#FFBB00: $A\in$ it |
| @#AAFFAA: inclusion   | @#AAFFAA: $A\subseteq$ atlas ($\langle M,T\rangle,n$) |
| @#FFFDDD: forall      | @#FFFDDD: $\langle V,\phi\rangle,\langle W,\psi\rangle\in A$ |
| @#55EE55: postulate   | @#55EE55: $\phi\circ\psi^{-1}$ ... smooth |

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.

=== Universal property ===
For a smooth atlas there are smooth coordinate changes on $\mathbb R^n$.

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=== Idea ===
For a smooth atlas there are smooth coordinate changes on $\mathbb R^n$.

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=== Context* ===
[[Second-countable Hausdorff space]], [[Natural number]]
=== Subset of ===
[[Atlas]]
=== Requirements ===
[[Smooth function]]