# Definition:Coordinate Function

## Definition

Let $M$ be a locally Euclidean space of dimension $n$.

Let $\struct {U, \kappa}$ be a coordinate chart.

Let $\pr_i: \R^n \to \R$ be the $i$th projection.

Then the mapping $\kappa_i$, defined as:

$\kappa_i = \pr_i \circ \kappa: U \to \map {\paren {\pr_i \circ \kappa} } U \subseteq \R$

is called the $i$th coordinate function on $U$.