Definition:Metric Induced by Norm on Division Ring

Definition

Let $\struct {R, \norm {\,\cdot\,} }$ be a normed division ring.

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

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

Also see

• Metric Induced by Norm on Normed Division Ring is Metric

Sources

• 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction ... (previous) ... (next): $\S 2.3$: Topology: Definition $2.3.1$