Definition:Chart

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

A chart of $M$ is an ordered pair $\left({U, \phi}\right)$, where:


 * $U$ is an open connected subset of $M$
 * $\phi: U \to D$ is a homeomorphism of $U$ onto an open subset $D$ of Euclidean space.

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.