In mathematics, Fréchet filter is an important concept in order theory. Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote quotations related to: Mathematics Look up Mathematics in Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... Order theory is a branch of mathematics that studies various kinds of binary relations that capture the intuitive notion of a mathematical ordering. ...

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. Maurice Fréchet (born September 2, 1878, died June 4, 1973) was a French mathematician. ... In mathematics, a filter is a special subset of a partially ordered set. ... The notion of a set is one of the most important and fundamental concepts in modern mathematics. ... A is a subset of B If X and Y are sets and every element of X is also an element of Y, then we say or write: X is a subset of (or is included in) Y; X ⊆ Y; Y is a superset of (or includes) X; Y ⊇ X... In set theory and other branches of mathematics, two kinds of complements are defined, the relative complement and the absolute complement. ...

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. Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), or they can be used for ordering (this is...

See also

• filter (mathematics)