##  [Arzela-Ascoli Theorem](/index.php/arzela-ascoli-theorem) 

  ##  [Arzela-Ascoli Theorem](https://puremath.quantumdictionary.io/arzela-ascoli-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A characterization of relatively compact subsets of C(K) (continuous real- or complex-valued functions on a compact domain K) under the uniform topology: a family is relatively compact if and only if it is equicontinuous and pointwise relatively compact (often stated as equicontinuous and pointwise bounded).