\begin{definition}[Definition:Contour/Image]
Let $\R^n$ be a real cartesian space of $n$ dimensions.
Let $C$ be a '''contour''' in $\R^n$ defined by the (finite) sequence $\sequence {C_1, \ldots, C_n}$ of directed smooth curves in $\R^n$.
Let $C_i$ be parameterized by the smooth path $\rho_i: \closedint {a_i} {b_i} \to \R^n$ for all $i \in \set {1, \ldots, n}$.
The '''image of $C$''' is defined as:
:$\ds \Img C := \bigcup_{i \mathop = 1}^n \Img {\rho_i}$
where $\Img {\rho_i}$ denotes the image of $\rho_i$.
\end{definition}