# Definition:Complete Disconnected Riemannian Manifold

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## Definition

Let $\struct {M, g}$ be a disconnected Riemannian manifold.

Suppose $M$ is geodesically complete or that every disconnected component is a complete metric space.

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Then $M$ is said to be **complete**.

## Sources

- 2018: John M. Lee:
*Introduction to Riemannian Manifolds*(2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Completeness