Theorems · Theorem · algebraic geometry
AlgebraicGeometry.surjective_of_isDominant_of_isClosed_range
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsDominant f],
IsClosed (Set.range ⇑f) → AlgebraicGeometry.Surjective f- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsDominant
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Set.rangestatement and proof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- Set.univproof · cited by 3,945
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ext_of_isDominant_of_isSeparatedproof · cited by 3