Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.self_le_iSup_basicOpen_iff
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens},
AlgebraicGeometry.IsAffineOpen U →
∀ {s : Set ↑(X.presheaf.obj (Opposite.op U))}, U ≤ ⨆ f, X.basicOpen ↑f ↔ Ideal.span s = ⊤- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topstatement · cited by 9,680
- Oppositestatement · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- Idealstatement · cited by 4,748
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- iSupstatement and proof · cited by 2,415
- CommRingCatstatement · cited by 2,333
- le_antisymmproof · cited by 2,068
- TopologicalSpace.Opensstatement · cited by 2,040
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.of_affine_open_coverproof · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.le_of_iSup_eq_topproof · cited by 1