Definition:Complete Normed Division Ring

From ProofWiki
Jump to navigation Jump to search

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