##  [Jordan Curve Theorem](/jordan-curve-theorem) 

  ##  [Jordan Curve Theorem](https://mathlogic.quantumdictionary.io/jordan-curve-theorem-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Topological theorem asserting that every simple closed curve (a continuous injective image of the circle) in the plane separates the plane into exactly two regions: an interior bounded region and an exterior unbounded region, with the curve as their common boundary.

 

 

 

 

 





 

 



 ##  [Jordan Curve Theorem](https://puremath.quantumdictionary.io/jordan-curve-theorem-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem asserting that every simple closed curve (a continuous embedding of the circle S^1) in the plane separates the plane into exactly two connected components, one bounded (the inside) and one unbounded (the outside), with the curve as their common boundary.