##  [Heine–Borel Theorem](/heine-borel-theorem) 

  ##  [Heine–Borel Theorem](https://mathlogic.quantumdictionary.io/heine-borel-theorem-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

In Euclidean space R^n, a subset is compact (every open cover has a finite subcover) if and only if it is closed and bounded; this characterizes compact sets in the standard topology on R^n.