Theorems · Theorem · general topology
TopCat.GlueData.isOpen_iff
∀ (D : TopCat.GlueData) (U : Set ↑D.glued), IsOpen U ↔ ∀ (i : D.J), IsOpen (⇑(CategoryTheory.ConcreteCategory.hom (D.ι i)) ⁻¹' U)
- Defined in
- Mathlib.Topology.Gluing
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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
- Setstatement and proof · cited by 53,352
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Set.preimagestatement and proof · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- ContinuousMapstatement · cited by 2,491
- CategoryTheory.Discreteproof · cited by 2,447
- IsOpenstatement and proof · cited by 2,400
- TopCatstatement · cited by 1,889
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Discrete.functorproof · cited by 633
Cited by3
Results whose statement or proof uses this declaration.
- TopCat.GlueData.open_image_openproof · cited by 1
- TopCat.GlueData.fromOpenSubsetsGlue_isOpenMapproof · cited by 1
- AlgebraicGeometry.Scheme.GlueData.isOpen_iffproof · cited by 1