Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.isCompact
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens}, AlgebraicGeometry.IsAffineOpen U → IsCompact ↑U- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 146 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
- Setproof · cited by 53,352
- TopologicalSpaceproof · cited by 24,529
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- Set.univproof · cited by 3,945
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
Cited by17
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.ker_applyproof · cited by 14
- AlgebraicGeometry.exists_appTop_π_eq_of_isLimitproof · cited by 2
- AlgebraicGeometry.isAffine_of_isAffineOpen_basicOpenproof · cited by 2
- AlgebraicGeometry.exists_eq_pow_mul_of_isCompact_of_isQuasiSeparatedproof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.of_isOpenMapproof · cited by 1
- AlgebraicGeometry.exists_isAffineOpen_preimage_eqproof · cited by 1
- AlgebraicGeometry.quasiSeparatedSpace_iff_forall_affineOpensproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.coequifibered_normalizationDiagramMapproof · cited by 1
- AlgebraicGeometry.exists_preimage_eqproof · cited by 1
- AlgebraicGeometry.isIso_pushoutSection_of_isQuasiSeparated_of_flat_rightproof · cited by 1
- AlgebraicGeometry.QuasiCompactCover.exists_isAffineOpen_of_isCompactproof · cited by 1