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
Parents
Context
Requirements
