Countable space with cofinite topology

Definition
This topological space is defined as follows:


 * Its underlying set is an infinite countable set.
 * The topology on it is a cofinite topology.

The topological space also arises as the Zariski topology for a countably infinite field as an algebraic variety over itself, or more generally, for any connected one-dimensional algebraic variety over a countably infinite field. Equivalently, it arises as the max-spectrum of the polynomial ring in one variable over a countably infinite field.