---
tag: QN98V7NMCD
kind: concept
name: Fréchet filter
aliases: [cofinite-filter]
sources:
  - wikipedia: en:1586291@r1324787022
    locator: Fréchet filter
    note: adopted
    mention: wikipedia://en/1586291
    sections: [Summary]
same_as:
  wikidata: Q1471386
  wikipedia: Fréchet filter
inventory: [FZZT2KT60R]
---

## Summary

In mathematics, the **Fréchet filter**, also called the **cofinite filter**, on a [[set|0BSJ7RQ9BW]] $X$ is a certain collection of subsets of $X$ (that is, it is a particular subset of the [[power set|00E0YZCERH]] of $X$). A subset $F$ of $X$ belongs to the Fréchet filter if and only if the [[complement|0RKF1ZT5JJ]] of $F$ in $X$ is finite. Any such set $F$ is said to be [[cofinite|1EZAT5BEVJ]] in $X$, which is why it is alternatively called the *cofinite filter* on $X$.