In mathematics, a cocountable subset whose complement is a countable set is cofinite.

σ-algebras

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. It is the smallest σ-algebra containing every singleton set.

Topology

The cocountable topology consists of the empty set.

References