Zariski topology

In algebraic geometry, the Zariski topology is a way of defining open and closed sets on an algebraic variety, where closed sets are the solution sets of polynomial equations.

Unlike familiar topologies, Zariski open sets are large and dense—the complement of a curve in a plane is open.

This coarseness makes it useful for studying algebraic rather than geometric properties: The Zariski topology on affine space has surprisingly few open sets.