# Carathéodory's theorem

> theorem in complex analysis that a conformal mapping sending the unit disk to a region in the complex plane bounded by a Jordan curve extends continuously to a homeomorphism from the unit circle onto the Jordan curve

**Wikidata**: [Q4378889](https://www.wikidata.org/wiki/Q4378889)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Carathéodory's_theorem_(conformal_mapping))  
**Source**: https://4ort.xyz/entity/carath-odory-s-theorem-q4378889