##  [Brouwer Fixed Point Theorem](/brouwer-fixed-point-theorem) 

  ##  [Brouwer Fixed Point Theorem](https://puremath.quantumdictionary.io/brouwer-fixed-point-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A theorem asserting that every continuous map from a closed ball in Euclidean n-space to itself has at least one fixed point; equivalently, any continuous function f : D^n → D^n satisfies f(x)=x for some x in D^n.