Theorems · Theorem · algebraic geometry
PrimeSpectrum.iSup_basicOpen_eq_top_iff
∀ {R : Type u} [inst : CommSemiring R] {ι : Type u_1} {f : ι → R},
⨆ i, PrimeSpectrum.basicOpen (f i) = ⊤ ↔ Ideal.span (Set.range f) = ⊤- Cited by
- 6 results in Mathlib
- Foundations
- Depth 81 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.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Idealstatement · cited by 4,748
- Set.rangestatement and proof · cited by 4,705
- Set.univproof · cited by 3,945
- Compl.complproof · cited by 2,925
- Set.iUnionproof · cited by 2,483
- iSupstatement · cited by 2,415
- TopologicalSpace.Opensstatement · cited by 2,040
- Ideal.spanstatement and proof · cited by 948
Cited by6
Results whose statement or proof uses this declaration.
- Algebra.IsLocalIso.of_span_range_eq_topproof · cited by 3
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- PrimeSpectrum.iSup_basicOpen_eq_top_iff'proof · cited by 2
- PrimeSpectrum.toPiLocalization_surjective_of_discreteTopologyproof · cited by 2
- AlgebraicGeometry.essentiallySmall_costructuredArrow_Specproof · cited by 0