Definition:Coordinate Function

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

Let $\left( {U, \kappa} \right)$ be a chart.

Let $\mathrm{pr}^i\colon \R^n \to \R$ be the $i$th projection.

Then the mapping $\kappa^i$ defined as
 * $\displaystyle \mathrm{pr}^i \circ \kappa : U \to \mathrm{pr}^i \circ \kappa \left( { U } \right) \subseteq \R$

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