Fréchet filter

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In mathematics, Fréchet filter is an important concept in order theory.

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,∞) : nN} 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.

[edit] See also

• filter (mathematics)