---
tag: 0KZZ70ZHXP
kind: concept
name: Diffeomorphism
aliases: [smooth-isomorphism]
msc: [58C25]
uses: [0HHHDCXZV4, 0JPCHTXWG0]
sources:
  - url: https://en.wikipedia.org/wiki/Diffeomorphism
    locator: Definition
same_as:
  wikidata: Q1058314
  wikipedia: Diffeomorphism
---

## Summary

A diffeomorphism is a bijection between open sets, or between manifolds, such that both the map and its inverse are [[differentiable|0HHHDCXZV4]].
Diffeomorphisms are the changes of coordinates of calculus, and they preserve all differentiable structure.