Zariski topology

The Zariski topology is a topological space $({\mathbb{C}}^n,\tau )$ with closed sets $\{V(I)\}$ which are the vanishing loci of algebra ideals of $\mathbb{C}[x_1,\dots ,x_n]$

(though this can be done for ${\mathbb{F}}^n$ for an algebraically closed field).