Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.irreducibleComponentOpen_eq_top
∀ (X : AlgebraicGeometry.Scheme),
∀ Z ∈ irreducibleComponents ↥X,
∀ [inst : AlgebraicGeometry.IsNoetherian X] [IrreducibleSpace ↥X], X.irreducibleComponentOpen Z = ⊤- Cited by
- 0 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Top.topstatement and proof · cited by 9,680
- Set.univproof · cited by 3,945
- TopCat.carrierstatement and proof · cited by 3,184
- Compl.complproof · cited by 2,925
- 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
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
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