Smooth atlas
Set
| context | ⟨M,T⟩ … second-countable Hausdorff space |
| context | n∈N |
| definiendum | A∈ it |
| inclusion | A⊆ atlas (⟨M,T⟩,n) |
| forall | ⟨V,ϕ⟩,⟨W,ψ⟩∈A |
| postulate | ϕ∘ψ−1 … smooth |
A priori “ϕ∘ψ−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 Rn.
Idea
For a smooth atlas there are smooth coordinate changes on Rn.
Context*
Subset of
Requirements
