Definition:Chart

Definition
Let $M$ be a topological manifold of dimension $d$.

A $d$-dimensional chart of $M$ is an ordered pair $\struct {U, \phi}$, where:


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

Also defined as
The open set $U$ is sometimes required to be connected.

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

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

Also see

 * Definition:Transition Mapping between Charts
 * Definition:Atlas
 * Definition:Locally Euclidean Space