Definition:Complete Normed Division Ring
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Definition
A normed division ring $\struct {R, \norm {\, \cdot \,} }$ is complete if and only if the metric space $\struct {R, d}$ is a complete metric space where $d$ is the metric induced by the norm $\norm {\, \cdot \,}$.
That is, a normed division ring $\struct {R, \norm {\, \cdot \,} }$ is complete if and only if every Cauchy sequence is convergent.
Sources
- 1997: Fernando Q. Gouvea: p-adic Numbers: An Introduction ... (previous) ... (next): $\S 3.2$: Completions