Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isCompact_basicOpen
∀ (X : AlgebraicGeometry.Scheme) {U : X.Opens},
IsCompact ↑U → ∀ (f : ↑(X.presheaf.obj (Opposite.op U))), IsCompact ↑(X.basicOpen f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
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
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.Functor.mapproof · cited by 8,698
- SetLike.coestatement and proof · cited by 8,199
- Oppositestatement · cited by 8,081
- Set.Elemproof · cited by 7,166
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- Finiteproof · cited by 3,029
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1