Definition:Complete Metric Space/Definition 2

Definition

A metric space $M = \struct {A, d}$ is complete if and only if the intersection of every nested sequence of closed balls whose radii tend to zero is non-empty.

Also see

• Equivalence of Definitions of Complete Metric Space

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $5$: Metric Spaces: Complete Metric Spaces