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

• Results about Zariski topology can be found here.

Source of Name

This entry was named for Oscar Zariski.