Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.IsQuasiAffine.of_forall_exists_mem_basicOpen
∀ (X : AlgebraicGeometry.Scheme) [CompactSpace ↥X], (∀ (x : ↥X), ∃ r, AlgebraicGeometry.IsAffineOpen (X.basicOpen r) ∧ x ∈ X.basicOpen r) → X.IsQuasiAffine
A quasi-compact scheme is quasi-affine if it can be covered by affine basic opens of global sections.
- Defined in
- Mathlib.AlgebraicGeometry.QuasiAffine
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompactSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.Functor.mapproof · cited by 8,698
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.homproof · cited by 7,684
- TopCat.carrierstatement and proof · 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 and proof · cited by 2,020
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IsQuasiAffine.of_isAffineHomproof · cited by 2
- AlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimitproof · cited by 1