# Definition:Chart

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## Definition

Let $M$ be a locally Euclidean space, or complex locally Euclidean space 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 system or coordinate neighborhood.

The danger of confusion with other notions of coordinate renders the latter inadequate for use on $\mathsf{Pr} \infty \mathsf{fWiki}$.