Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.isBasis_affineOpens
∀ (X : AlgebraicGeometry.Scheme), TopologicalSpace.Opens.IsBasis X.affineOpens
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensproof · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
Cited by37
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.iSup_affineOpens_eq_topproof · cited by 13
- AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalkproof · cited by 8
- AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalkproof · cited by 6
- AlgebraicGeometry.Scheme.Hom.range_subset_ker_supportproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealproof · cited by 4
- AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locallyproof · cited by 3
- AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalkproof · cited by 3
- AlgebraicGeometry.iSup_basicOpen_of_span_eq_topproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIsoproof · cited by 2
- AlgebraicGeometry.Scheme.fromSpecStalk_appproof · cited by 2
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2