Definition:Ultrametric Space

Definition

An ultrametric space is a metric space $\struct {X, d}$ where $d$ is non-Archimedean.

Also see

• Definition:Non-Archimedean Metric

• Definition:Metric Space

Sources

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

• 2007: Svetlana Katok: p-adic Analysis Compared with Real ... (previous) ... (next): $\S 1.2$ Normed fields: Remark $1.13$