---
tag: 0QW64ARSHB
kind: concept
name: Simply connected domain
aliases: [simply-connected-space]
msc: [55Q05]
sources:
  - url: https://en.wikipedia.org/wiki/Simply_connected_space
    locator: lead section
same_as:
  wikidata: Q912058
  wikipedia: Simply connected space
---

## Summary

A simply connected domain is a path-connected set in which each closed loop can be shrunk continuously to a point without leaving the set.
Informally, the set is in one piece and has no hole that a loop can go around.
On such domains, curl-free vector fields are conservative.