Definition:Zariski Topology

Definition
Let $F$ be a field.

The Zariski topology is the topology on the direct product $F^n$ which sets:
 * $X \subset F^n$ is open $\iff F^n \setminus X$ is an affine algebraic variety

where $F^n \setminus X$ denotes set difference.

This topology is useful because it takes a purely algebraic object, that is a field, and defines it as a geometric object.