Cocountable topology

Cocountable topology is a specific type of topology defined on a set where a subset is considered open if it is either empty or its complement is a countable set. More formally, let \( X \) be a set. The cocountable topology on \( X \) is defined by specifying that the open sets are of the form \( U \subseteq X \) such that either: 1. \( U = \emptyset \), or 2.