An important, but not Hausdorff, topology in algebraic geometry. In the Zariski topology on ℂⁿ a closed subset is one of the form

where I ⊆ ℂ[x₁,x₂,…,x_n]. The Zariski topology on complex projective space can be similarly defined using homogeneous polynomials. The Zariski topology on any affine or projective variety is then the subspace topology induced by the ambient space.