Category:Metrics Induced by Norms

This category contains results about Metrics Induced by Norms.
Definitions specific to this category can be found in Definitions/Metrics Induced by Norms.

Let $V$ be a normed vector space.

Let $\norm {\,\cdot\,}$ be the norm of $V$.

Then the induced metric or the metric induced by $\norm {\,\cdot\,}$ is the mapping $d: V \times V \to \R_{\ge 0}$ defined as:

$\map d {x, y} = \norm {x - y}$