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- A topological space that is Noetherian (every open set is quasicompact)
- A topological space that is Noetherian and also sober (every nonempty closed irreducible subset is the closure of a unique point). The spectrum of any commutative Noetherian ring is a Zariski space in this sense
- A Zariski–Riemann space of valuations of a field
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