Definition:Coordinate Function

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

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

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

Then the mapping $\kappa^i$, defined as:


 * $\displaystyle \kappa^i = \mathrm{pr}^i \circ \kappa : U \to \left({\mathrm{pr}^i \circ \kappa \left({U}\right)}\right) \subseteq \R$

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