The Zariski topology on an affine scheme has closed sets for ideals . Its basic open sets are the principal open subschemes .
A subset of an algebraic variety is Zariski dense when its closure in the Zariski topology is the whole variety. For an affine variety, this is equivalent to saying that every regular function vanishing on the subset vanishes on the entire variety.
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Zariski topology is a type of topology that is used primarily in algebraic geometry and algebraic varieties. It is defined on the set of points that correspond to solutions of polynomial equations. ### Key Aspects of Zariski Topology: 1. **Basic Idea**: In Zariski topology, the closed sets are defined by polynomials.