Theorems · Theorem · algebraic geometry
AlgebraicGeometry.LocallyRingedSpace.basicOpen_zero
∀ (X : AlgebraicGeometry.LocallyRingedSpace) (U : TopologicalSpace.Opens ↑↑X.toPresheafedSpace), X.toRingedSpace.basicOpen 0 = ⊥
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
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 · cited by 19,642
- SetLike.coeproof · cited by 8,199
- Oppositestatement · cited by 8,081
- Set.ofPredproof · cited by 6,101
- Bot.botstatement · cited by 4,720
- 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
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.basicOpen_zeroproof · cited by 3
- AlgebraicGeometry.LocallyRingedSpace.basicOpen_eq_bot_of_isNilpotentproof · cited by 1