Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_self
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U),
(TopologicalSpace.Opens.map hU.fromSpec.base).obj U = ⊤- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- 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
Cited by10
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpenproof · cited by 18
- AlgebraicGeometry.IsAffineOpen.fromSpec_app_selfstatement · cited by 6
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_appproof · cited by 5
- AlgebraicGeometry.IsAffineOpen.isLocalization_stalk'proof · cited by 2
- AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iffproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.ΓSpecIso_hom_fromSpec_appstatement · cited by 1
- AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen'proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.fromNormalization_appproof · cited by 1
- AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_applystatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.normalization.hom_extproof · cited by 0