| context | $\langle M,T_X\rangle$ … second-countable Hausdorff space |
| context | $n\in \mathbb N$ |
| let | $\langle \mathbb R^n,T_{\mathbb R^n}\rangle$ … Euclidean topology |
| definiendum | $\langle U,\phi\rangle\in$ it |
| inclusion | $U\in T_M$ |
| exists | $U_{\mathbb R^n}\in T_{\mathbb R^n}$ |
| inclusion | $\phi:U\to U_{\mathbb R^n}$ |
| inclusion | $\phi$ … homeomorphism |
The charts on $M$ are the homeomorphism into $\mathbb R^n$.