Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isCompact_preimage_singleton
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.QuasiCompact f] (y : ↥Y), IsCompact (⇑f ⁻¹' {y})- Defined in
- Mathlib.AlgebraicGeometry.Fiber
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Set.preimagestatement · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singletonproof · cited by 1
- AlgebraicGeometry.QuasiCompact.isCompact_preimage_singletonproof · cited by 0