Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.GlueData.isOpen_iff
∀ (D : AlgebraicGeometry.Scheme.GlueData) (U : Set ↥D.glued), IsOpen U ↔ ∀ (i : D.J), IsOpen (⇑(D.ι i) ⁻¹' U)
- Defined in
- Mathlib.AlgebraicGeometry.Gluing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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
- Quiver.Homproof · cited by 32,603
- 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
- AlgebraicGeometry.Schemestatement · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- IsOpenstatement and proof · cited by 2,400
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.isOpenMap_fromGluedproof · cited by 1