Definition:Chart

Definition
Let $M$ be a locally Euclidean space, or complex locally Euclidean space of dimension $d$.

Let $U \subseteq M$ be an open connected set that is homeomorphic to an open set $D$ of Euclidean space.

Let $\phi : U \to D$ be a particular homeomorphism.

Then the pair $\left({ U,\phi }\right)$ is called a chart of $M$.

Also known as
Some sources refer to a chart as a coordinate system.

The danger of confusion with other notions of coordinate renders the latter inadequate for use on this site.