##  [Filter](/filter) 

  ##  [Filter](https://puremath.quantumdictionary.io/filter-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A nonempty family F of subsets of a set X that is closed under finite intersections and under supersets (if A is in F and A ⊆ B ⊆ X then B is in F). Filters are used to express notions of largeness and to define convergence independent of countable indices.