Theorems · Theorem · general topology
TopCat.GlueData.fromOpenSubsetsGlue_isOpenMap
∀ {α : Type u} [inst : TopologicalSpace α] {J : Type u} (U : J → TopologicalSpace.Opens α),
IsOpenMap ⇑(CategoryTheory.ConcreteCategory.hom (TopCat.GlueData.fromOpenSubsetsGlue U))- Defined in
- Mathlib.Topology.Gluing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
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.Homproof · cited by 32,603
- TopologicalSpacestatement and proof · cited by 24,529
- CategoryTheory.Functor.objproof · cited by 19,642
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- IsOpenproof · cited by 2,400
Cited by2
Results whose statement or proof uses this declaration.
- TopCat.GlueData.openCoverGlueHomeoproof · cited by 0
- TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbeddingproof · cited by 0