## 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)