# Category:Zariski Topology

This category contains results about Zariski Topology.

Definitions specific to this category can be found in Definitions/Zariski Topology.

### On an Affine Space

Let $k$ be a field.

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

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

### On the spectrum of a ring

Let $A$ be a commutative ring with unity.

Let $\operatorname{Spec} \left({A}\right)$ be the prime spectrum of $A$.

The **Zariski topology** on $\operatorname{Spec} A$ is the topology with closed sets the vanishing sets $V \left({S}\right)$ for $S \subseteq A$.

## Pages in category "Zariski Topology"

This category contains only the following page.