##  [Jordan–Brouwer Separation Theorem](/jordan-brouwer-separation-theorem) 

  ##  [Jordan–Brouwer Separation Theorem](https://puremath.quantumdictionary.io/jordan-brouwer-separation-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A generalization of the Jordan curve theorem: an embedding of an (n−1)-sphere S^{n−1} in Euclidean n-space R^n separates R^n into exactly two complementary regions, one bounded (the 'inside') and one unbounded (the 'outside'), and the embedded sphere is their common boundary.