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Noetherian Zariski topology

The Zariski topology on affine space is Noetherian because polynomial rings are Noetherian. Every closed subset is a finite union of irreducible closed subsets: a minimal counterexample would split into two smaller closed subsets, each already having such a decomposition.

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  1. Irreducible topological space
  2. Algebraic geometry
  3. Geometry and topology
  4. Area of mathematics
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