Definition:Metric Induced by Norm on Division Ring
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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
Sources
- 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction ... (previous) ... (next): $\S 2.3$: Topology: Definition $2.3.1$