Chart

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 $\mathbb R^n$ .