# Hopf–Rinow theorem

> theorem that, for a Riemannian manifold, geodesic completeness is equivalent to completeness as a metric space

**Wikidata**: [Q2094241](https://www.wikidata.org/wiki/Q2094241)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Hopf–Rinow_theorem)  
**Source**: https://4ort.xyz/entity/hopf-rinow-theorem


## References

1. Freebase Data Dumps. 2013