## Smooth manifold

### Set

context | $\langle M,T\rangle$ … second-countable Hausdorff space |

context | $n\in \mathbb N$ |

definiendum | $\langle M,A\rangle\in$ it |

postulate | $A$ 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: Differentiable manifold