Definition:Smooth Path/Closed/Real Cartesian Space
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Definition
Let $\R^n$ be a real cartesian space of $n$ dimensions.
Let $\left[{a \,.\,.\, b}\right]$ be a closed real interval.
Let $\rho: \left[{a \,.\,.\, b}\right] \to \R^n$ be a smooth path in $\R^n$.
$\rho$ is a closed smooth path if and only if $\rho$ is a closed path.
That is, if and only if $\rho \left({a}\right) = \rho \left({b}\right)$.
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