Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isBasis_basicOpen
∀ (X : AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsAffine X], TopologicalSpace.Opens.IsBasis (Set.range X.basicOpen)
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsAffine
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpaceproof · cited by 24,529
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Oppositestatement · cited by 8,081
- Set.ofPredproof · cited by 6,101
- Set.preimageproof · cited by 4,946
- Set.rangestatement and proof · cited by 4,705
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.exists_basicOpen_leproof · cited by 5
- AlgebraicGeometry.stalkMap_injective_of_isOpenMap_of_injectiveproof · cited by 0