Cocountability

In mathematics, a cocountable subset of a set "X" is a subset "Y" whose complement in "X" is a countable set. In other words, "Y" contains all but countably many elements of "X". While 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 "Y" is cofinite.
σ-algebras.
The set of all subsets of "X" 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 "X". It is the smallest σ-algebra containing every singleton set.
Topology.
The cocountable topology (also called the "countable complement topology") on any set "X" consists of the empty set and all cocountable subsets of "X".