Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isCompact_preimage
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f] {U : Y.Opens},
IsCompact ↑U → IsCompact ↑((TopologicalSpace.Opens.map f.base).obj U)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- SetLike.coestatement and proof · cited by 8,199
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- IsCompactstatement and proof · cited by 1,282
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.coequifibered_normalizationDiagramMapproof · cited by 1