##  [Hahn-Banach Theorem](/hahn-banach-theorem-1) 

  ##  [Hahn-Banach Theorem](https://puremath.quantumdictionary.io/hahn-banach-theorem-2) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A family of extension results that guarantee a bounded linear functional defined on a linear subspace of a real or complex normed vector space can be extended to the whole space without increasing its norm; equivalent algebraic forms cover extension dominated by a sublinear functional.