Theorems · Theorem · algebraic geometry
PrimeSpectrum.isClosed_iff_zeroLocus
∀ {R : Type u} [inst : CommSemiring R] (Z : Set (PrimeSpectrum R)), IsClosed Z ↔ ∃ s, Z = PrimeSpectrum.zeroLocus s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CommSemiringstatement and proof · cited by 10,911
- Compl.complproof · cited by 2,925
- IsClosedstatement · cited by 1,639
- PrimeSpectrumstatement and proof · cited by 625
- compl_complproof · cited by 229
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- isOpen_compl_iffproof · cited by 63
- PrimeSpectrum.isOpen_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
- PrimeSpectrum.isClosed_zeroLocusproof · cited by 10
- PrimeSpectrum.isClosed_image_of_stableUnderSpecializationproof · cited by 6
- PrimeSpectrum.isClosed_iff_zeroLocus_idealproof · cited by 4