Frechet filterの英wikipedia記事と ”Examples On the set N of natural numbers, the set of infinite intervals B = { (n,∞) : n ∈ N} is a Frechet filter base, i.e., the Frechet filter on N consists of all supersets of elements of B.” あと、MathWorld ”Cofinite Filter If S is an infinite set, then the collection F_S={ A ⊆ S:S-A is finite} is a filter called the cofinite (or Frechet) filter on S.”
（参考） https://en.wikipedia.org/wiki/Fr%C3%A9chet_filter Frechet filter (抜粋) In mathematics, the Frechet filter, also called the cofinite filter, on a set is a special subset of the set's power set. A member of this power set is in the Frechet filter if and only if its complement in the set is finite. This is of interest in topology, where filters originated, and relates to order and lattice theory because a set's power set is a partially ordered set (and more specifically, a lattice) under set inclusion.
The Frechet filter is named after the French mathematician Maurice Frechet (1878-1973), who worked in topology. It is alternatively called a cofinite filter because its members are exactly the cofinite sets in a power set.
Contents 1 Definition 2 Properties 3 Examples 4 See also 5 References
Examples On the set N of natural numbers, the set of infinite intervals B = { (n,∞) : n ∈ N} is a Frechet filter base, i.e., the Frechet filter on N consists of all supersets of elements of B.[citation needed]
External links ・Weisstein, Eric W. "Cofinite Filter". MathWorld. https://mathworld.wolfram.com/CofiniteFilter.html Cofinite Filter If S is an infinite set, then the collection F_S={ A ⊆ S:S-A is finite} is a filter called the cofinite (or Frechet) filter on S.
