##  [Open Cover Refinement](/open-cover-refinement) 

  ##  [Open Cover Refinement](https://puremath.quantumdictionary.io/open-cover-refinement-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A process in topology that replaces an open cover of a space by another open cover in which every set of the new cover is contained in some set of the original cover; used to obtain covers with additional properties (e.g., locally finite, subordinate to a partition of unity).