Definition:Coordinate Function

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

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

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

Then the mapping $\kappa_i$, defined as:


 * $\kappa_i = \operatorname{pr}_i \mathop \circ \kappa: U \to \left({\operatorname{pr}_i \mathop \circ \kappa \left({U}\right)}\right) \subseteq \R$

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