In mathematics, a cofinite subset of a set X {\displaystyle X} is a subset A {\displaystyle A} whose complement in X {\displaystyle X} is a finite set...

In mathematics, the Fréchet filter, also called the cofinite filter, on a set X {\displaystyle X} is a certain collection of subsets of X {\displaystyle...

of all the open sets containing it. Every finite set is closed. Every cofinite set of X {\displaystyle X} is open. For every x ∈ X , {\displaystyle x\in...

topology Cocountable topology Cofinite topology Compact-open topology Compactification Discrete topology Double-pointed cofinite topology Extended real number...

a cofinite set with any set is cofinite, while the union of two finite sets is finite. Intersection behaves like union with "finite" and "cofinite" interchanged...

cocountable subset of the reals. If the complement is finite, then one says Y is cofinite. The set of all subsets of X that are either countable or cocountable forms...

A simple example of a topology that is T1 but is not Hausdorff is the cofinite topology defined on an infinite set, as is the cocountable topology defined...

finite or cofinite is a Boolean algebra and an algebra of sets called the finite–cofinite algebra. If S is infinite then the set of all cofinite subsets...

{\displaystyle \mathbb {1} _{S}} is computable. Examples: Every finite or cofinite subset of the natural numbers is computable. This includes these special...

Hausdorff spaces where limit points are unique. Any set can be given the cofinite topology in which the open sets are the empty set and the sets whose complement...