Theorems · Theorem · algebraic geometry
PrimeSpectrum.isClosed_of_stableUnderSpecialization_of_isConstructible
∀ {R : Type u_4} [inst : CommRing R] {s : Set (PrimeSpectrum R)},
StableUnderSpecialization s → Topology.IsConstructible s → IsClosed s[Stacks Tag 00I0](https://stacks.math.columbia.edu/tag/00I0) ((1))
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- RingHomproof · cited by 10,189
- Set.rangeproof · cited by 4,705
- IsClosedstatement · cited by 1,639
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.comapproof · cited by 199
- Topology.IsConstructiblestatement and proof · cited by 45
- StableUnderSpecializationstatement and proof · cited by 32
- PrimeSpectrum.isClosed_range_of_stableUnderSpecializationproof · cited by 2
- PrimeSpectrum.exists_range_eq_of_isConstructibleproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isOpen_of_stableUnderGeneralization_of_isConstructibleproof · cited by 1