Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isAffineOpen_top
∀ (X : AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsAffine X], AlgebraicGeometry.IsAffineOpen ⊤
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsAffine
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.IsAffineOpenstatement and proof · cited by 222
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
Cited by27
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.Spec.fromSpecStalk_eqproof · cited by 4
- AlgebraicGeometry.IsAffineOpen.fromSpec_topstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalkproof · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.ext_of_isAffinestatement and proof · cited by 3
- AlgebraicGeometry.HasRingHomProperty.appTopproof · cited by 3
- AlgebraicGeometry.IsAffineOpen.infproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.equivOfIsAffineproof · cited by 2
- AlgebraicGeometry.affineAnd_isLocalproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.Spec_basicOpenproof · cited by 2
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.le_of_isAffinestatement and proof · cited by 2