Definition:Zariski Topology

Definition
For a field $$F \ $$, the Zariski topology is the topology on the space $$F^n \ $$ which sets


 * $$X \subset F^n \ $$ is open $$\iff \ $$ $$F^n - X \ $$ is an affine algebraic variety.

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