Theorems · Theorem · category theory
TopologicalSpace.Opens.isOpenEmbedding
∀ {X : TopCat} (U : TopologicalSpace.Opens ↑X),
Topology.IsOpenEmbedding ⇑(CategoryTheory.ConcreteCategory.hom U.inclusion')- Defined in
- Mathlib.Topology.Category.TopCat.Opens
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- TopCatstatement and proof · cited by 1,889
- Topology.IsOpenEmbeddingstatement · cited by 231
- TopologicalSpace.Opens.is_open'proof · cited by 139
- TopologicalSpace.Opens.toTopCatstatement · cited by 81
- TopologicalSpace.Opens.inclusion'statement · cited by 73
- IsOpen.isOpenEmbedding_subtypeValproof · cited by 32
Cited by65
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpecstatement · cited by 13
- AlgebraicGeometry.ProjIsoSpecTopComponent.toSpecstatement · cited by 9
- TopologicalSpace.OpenNhds.isOpenEmbeddingproof · cited by 7
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrierstatement · cited by 5
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.mk_mem_carrierstatement and proof · cited by 5
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓstatement · cited by 5
- AlgebraicGeometry.PresheafedSpace.toRestrictTopstatement · cited by 4
- AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.toFunstatement · cited by 4
- TopologicalSpace.Opens.functor_map_eq_infstatement and proof · cited by 3
- TopologicalSpace.Opens.isOpenEmbedding_obj_topstatement · cited by 3
- AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFunstatement · cited by 3
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eqstatement and proof · cited by 3