Theorems · Theorem · algebraic geometry
AlgebraicGeometry.RingedSpace.basicOpen_mul
∀ (X : AlgebraicGeometry.RingedSpace) {U : TopologicalSpace.Opens ↑↑X.toPresheafedSpace}
(f g : ↑(X.presheaf.obj (Opposite.op U))), X.basicOpen (f * g) = X.basicOpen f ⊓ X.basicOpen g- Defined in
- Mathlib.Geometry.RingedSpace.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- SetLike.coeproof · cited by 8,199
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- Set.extproof · cited by 2,266
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- IsUnitproof · cited by 1,602
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.basicOpen_mulproof · cited by 6
- AlgebraicGeometry.RingedSpace.basicOpen_powproof · cited by 2