Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.affineBasisCover_is_basis
∀ (X : AlgebraicGeometry.Scheme), TopologicalSpace.IsTopologicalBasis {x | ∃ a, x = Set.range ⇑(X.affineBasisCover.f a)}- Defined in
- Mathlib.AlgebraicGeometry.Cover.Open
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Setstatement and proof · cited by 53,352
- SetLike.coeproof · cited by 8,199
- Set.ofPredstatement and proof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- IsOpenproof · cited by 2,400
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isBasis_affineOpensproof · cited by 37
- AlgebraicGeometry.reduce_to_affine_globalproof · cited by 1