Theorems · Theorem · algebraic geometry
AlgebraicGeometry.RingedSpace.basicOpen_of_isUnit
∀ (X : AlgebraicGeometry.RingedSpace) {U : TopologicalSpace.Opens ↑↑X.toPresheafedSpace}
{f : ↑(X.presheaf.obj (Opposite.op U))}, IsUnit f → X.basicOpen f = U- Defined in
- Mathlib.Geometry.RingedSpace.Basic
- Cited by
- 1 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.
Cites18
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
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- CommRingCatstatement · cited by 2,333
- le_antisymmproof · cited by 2,068
- 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
- IsUnitstatement and proof · cited by 1,602
- AlgebraicGeometry.PresheafedSpace.presheafstatement and proof · cited by 1,104
- CommRingCat.carrierstatement and proof · cited by 1,096
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.basicOpen_of_isUnitproof · cited by 3