 ##  [Compactness](/compactness) 

  ##  [Compactness](https://natural.quantumdictionary.io/compactness-0) 

  
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**Natural &amp; Formal Sciences Dictionary**

 
Definition

A topological property: a space is compact if every open cover admits a finite subcover; in metric spaces often equivalent to sequential compactness and to closedness plus boundedness in Euclidean settings.

 
 ##  [Compactness](https://mathlogic.quantumdictionary.io/compactness-1) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A topological property of a set meaning that every sequence in the set has a convergent subsequence whose limit lies in the set; equivalently in metric spaces, the set is sequentially compact.