Definition:Zariski Topology/Affine Space

Definition
Let $k$ be a field.

Let $\map {\mathbb A^n} k = k^n$ denote the standard affine space of dimension $n$ over $k$.

The Zariski topology on $\map {\mathbb A^n} k$ is the topology on the direct product $k^n$ whose closed sets are the affine algebraic sets in $\map {\mathbb A^n} k$.

Also see

 * Zariski Topology is Topology