Smooth atlas

Set

context $\langle M,T\rangle$ … second-countable Hausdorff space
context $n\in \mathbb N$
definiendum $A\in$ it
inclusion $A\subseteq$ atlas ($\langle M,T\rangle,n$)
forall $\langle V,\phi\rangle,\langle W,\psi\rangle\in A$
postulate $\phi\circ\psi^{-1}$ … smooth

A priori “$\phi\circ\psi^{-1}$” 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 $\mathbb R^n$.


Idea

For a smooth atlas there are smooth coordinate changes on $\mathbb R^n$.


Context*

Second-countable Hausdorff space, Natural number

Subset of

Atlas

Requirements

Smooth function