Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isOpenEmbedding
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [H : AlgebraicGeometry.IsOpenImmersion f], Topology.IsOpenEmbedding ⇑f- Defined in
- Mathlib.AlgebraicGeometry.OpenImmersion
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- 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
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- TopCatstatement · cited by 1,889
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
Cited by37
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.preimage_image_eqproof · cited by 37
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealproof · cited by 4
- AlgebraicGeometry.IsOpenImmersion.of_compproof · cited by 2
- AlgebraicGeometry.LocallyOfFiniteType.jacobsonSpaceproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_finite_preimage_singletonproof · cited by 2
- AlgebraicGeometry.Scheme.Modules.restrictStalkNatIsoproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- AlgebraicGeometry.isLocallyArtinian_iff_openCoverproof · cited by 2
- AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpenproof · cited by 2
- AlgebraicGeometry.Scheme.IsLocallyDirected.ι_jointly_surjectiveproof · cited by 1
- AlgebraicGeometry.quasiCompact_affineProperty_iff_quasiSeparatedSpaceproof · cited by 1