Cocountability


In mathematics, a cocountable subset of a set is a subset whose complement in is a countable set. In other words, contains all but countably many elements of. Since the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. If the complement is finite, then one says is cofinite.

σ-algebras

The set of all subsets of that are either countable or cocountable forms a σ-algebra, i.e., it is closed under the operations of countable unions, countable intersections, and complementation. This σ-algebra is the countable-cocountable algebra on. It is the smallest σ-algebra containing every singleton set.

Topology

The cocountable topology on any set consists of the empty set and all cocountable subsets of.