===== Smooth manifold =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $\langle M,T\rangle$ ... second-countable Hausdorff space |
| @#55CCEE: context     | @#55CCEE: $n\in \mathbb N$ |
| @#FFBB00: definiendum | @#FFBB00: $\langle M,A\rangle\in$ it |
| @#55EE55: postulate   | @#55EE55: $A$ maximal in smooth atlas($\langle M,T\rangle,n$) |

==== Discussion ====
=== Elaboration ===
Effectively, a smooth manifold would be given by providing //any// atlas. But then, due to the redundancy of some charts on small open sets, different atlases give rise to equivalent mathematical objects and so a smooth manifold is defined as the biggest and hence //unique// one amongst those objects.

=== Reference ====
Wikipedia: [[http://en.wikipedia.org/wiki/Differentiable_manifold|Differentiable manifold]]
==== Parents ====
=== Context ===
[[Second-countable Hausdorff space]]
=== Requirements ===
[[Smooth atlas]], [[Maximal extension in a set]]