Fréchet filter

If X is an infinite set, the Fréchet filter, also called cofinite filter on X, is the set of all subsets of X having finite complement in X.

For example, on the set N of natural numbers, the set B = { (n,∞) : n$in$N} is a Fréchet filter base, i.e. the Fréchet filter on N consists of all supersets of elements of B.

The Fréchet filter is an example of a free filter.

See also

• filter (mathematics)