Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt.isClopen_singleton_asFiber
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.LocallyOfFiniteType f] {x : ↥X},
AlgebraicGeometry.Scheme.Hom.QuasiFiniteAt f x → IsClopen {AlgebraicGeometry.Scheme.Hom.asFiber f x}- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
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- IsOpenproof · cited by 2,400
- 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 by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.quasiFiniteLocus_eq_top_iffproof · cited by 1