\begin{definition}[Definition:Coordinate Function]
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 $U$.
\end{definition}