## 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.