---
tag: 0ZV14XRNF0
kind: concept
name: Closed and exact forms
msc: [58A12]
uses: [0ZHSTAG8ZY, 0E3G0GRPZ6]
sources:
  - url: https://en.wikipedia.org/wiki/Closed_and_exact_differential_forms
    locator: lead section
same_as:
  wikidata: Q2100733
  wikipedia: Closed and exact differential forms
---

## Summary

A [[differential form|0E3G0GRPZ6]] is closed if its [[exterior derivative|0ZHSTAG8ZY]] is zero, and exact if it is the exterior derivative of another form.
Each exact form is closed. Whether each closed form is exact depends on the shape of the domain, so these notions detect holes in the domain.