##  [Tietze Extension Theorem](/tietze-extension-theorem) 

  ##  [Tietze Extension Theorem](https://puremath.quantumdictionary.io/tietze-extension-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

In a normal topological space, every continuous real-valued function defined on a closed subset extends to a continuous real-valued function on the whole space; bounded functions extend to bounded functions with the same bounds.