Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isClosed_singleton_iff_locallyOfFiniteType
∀ {X : AlgebraicGeometry.Scheme} [JacobsonSpace ↥X] {x : ↥X},
IsClosed {x} ↔ AlgebraicGeometry.LocallyOfFiniteType (X.fromSpecResidueField x)[Stacks Tag 01TB](https://stacks.math.columbia.edu/tag/01TB) ((1) => (2))
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- JacobsonSpace
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Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- 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
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- IsClosedstatement and proof · cited by 1,639
- CommRingCat.carrierproof · cited by 1,096
- AlgebraicGeometry.Specstatement · cited by 626
- AlgebraicGeometry.Scheme.residueFieldstatement and proof · cited by 95
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