Atlas
Set
| context | $\langle M,T\rangle$ … second-countable Hausdorff space |
| context | $n\in \mathbb N$ |
| definiendum | $A\in$ it |
| inclusion | $A\subseteq$ chart $\left(\langle M,T\rangle,n\right)$ |
| forall | $x\in M$ |
| exists | $\langle U,\varphi\rangle\in A$ |
| postulate | $x\in U$ |
Discussion
Idea
An atlas is a set of charts, so that no point $x\in M$ is left out from being mapped to $\mathbb R^n$.
Alternative definitions
One can equivalently postulate that $M$ is covered by the union of all the open subsets $U$ given with the charts $\langle U,\varphi\rangle$ of an atlas $A$:
$\bigcup_{chart\in A}\pi_1(chart)=M$.
Reference
Wikipedia: Atlas (topology)
Parents
Context*
Subset of
