##  [Alexander Subbase Theorem](/alexander-subbase-theorem) 

  ##  [Alexander Subbase Theorem](https://puremath.quantumdictionary.io/alexander-subbase-theorem-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A topological space is compact if every cover of the space by members of a subbase has a finite subcover: equivalently, if every open cover by subbasic open sets admits a finite subcover, then every open cover admits a finite subcover (compactness).