Definition:Smooth Path/Closed/Real Cartesian Space

Definition
Let $\R^n$ be a real cartesian space of $n$ dimensions. Let $\rho$ be a smooth path in $\R^n$.

$\rho$ is a closed smooth path $\rho$ is a closed path.

That is, $\rho \left({a}\right) = \rho \left({b}\right)$.