Theorems · Theorem · algebraic geometry
AlgebraicGeometry.range_eq_univ
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Surjective f], Set.range ⇑f = Set.univ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.Surjective
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Set.rangestatement · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- Set.univstatement · cited by 3,945
- TopCat.carrierstatement · 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 · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.range_subschemeιproof · cited by 4
- AlgebraicGeometry.range_eq_range_of_surjectiveproof · cited by 1
- AlgebraicGeometry.isIso_of_isClosedImmersion_of_surjectiveproof · cited by 1