---
tag: 0ZXSF2YQV2
kind: concept
name: Isometric isomorphism
aliases: [surjective-isometry, bijective-isometry]
msc: ["54E40"]
sources:
  - url: https://en.wikipedia.org/wiki/Isometry
    locator: Definition
---

## Summary

An isometric isomorphism is a bijective isometry between metric spaces.
Two metric spaces with an isometric isomorphism between them have the same metric properties.