---
tag: 06RW4RKWH7
kind: concept
name: Completion of a metric space
msc: ["54E50"]
sources:
  - url: https://en.wikipedia.org/wiki/Complete_metric_space
    locator: Completion
---

## Summary

The completion of a metric space is a complete metric space that contains an isometric copy of the space as a dense subset.
It is unique up to an isometric isomorphism that fixes the copy.