Definition:Complete Metric Space/Definition 2
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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
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