Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isClosed_singleton_iff_isClosedImmersion
∀ {X : AlgebraicGeometry.Scheme} {x : ↥X}, IsClosed {x} ↔ AlgebraicGeometry.IsClosedImmersion (X.fromSpecResidueField x)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- 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
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- IsClosedstatement and proof · cited by 1,639
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPointsproof · cited by 1
- AlgebraicGeometry.isClosed_singleton_iff_locallyOfFiniteTypeproof · cited by 0