Metric subspaces

By verifying the axioms, it can be shown that any subspace $ Y \subset X$ of a metric space $ (X,\rho)$ itself becomes a metric space by restricting the domain of $ \rho$ to $ Y \times Y$. This conveniently provides metrics on any of the manifolds and varieties from Chapter 4 by simply using any $ L_p$ metric on $ {\mathbb{R}}^m$, the space in which the manifold or variety is embedded.

Steven M LaValle 2012-04-20