AlgebraicGeometry.basicOpen_eq_bot_iff

∀ {X : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsReduced X] {U : X.Opens} (s : ↑(X.presheaf.obj (Opposite.op U))),
  X.basicOpen s = ⊥ ↔ s = 0

Defined in: Mathlib.AlgebraicGeometry.Properties
Cited by: 1 results in Mathlib
Foundations: Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.IsReduced

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Functor.objstatement and proof · cited by 19,642
Oppositestatement · cited by 8,081
Bot.botstatement and proof · cited by 4,720
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149

Results whose statement or proof uses this declaration.