Chart

Set

 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

Discussion

The charts on $M$ are the homeomorphism into $\mathbb R^n$.