Theorems · Theorem · algebraic geometry

AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompact

∀ {ι : Type u} (R : ι → CommRingCat) (U : (AlgebraicGeometry.Spec (CommRingCat.of ((i : ι) → ↑(R i)))).Opens)
  (V : Set ↥(AlgebraicGeometry.Spec (CommRingCat.of ((i : ι) → ↑(R i))))),
  ↑(AlgebraicGeometry.Scheme.Hom.opensRange (AlgebraicGeometry.sigmaSpec R)) ⊆ V → IsCompact V → V ⊆ ↑U → U = ⊤

Defined in: Mathlib.AlgebraicGeometry.PointsPi
Cited by: 1 results in Mathlib
Foundations: Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

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DFunLike.coeproof · cited by 62,936
Setstatement and proof · cited by 53,352
Quiver.Homstatement · cited by 32,603
CategoryTheory.Functor.objstatement · cited by 19,642
CategoryTheory.CategoryStruct.compproof · cited by 17,999
Finsetproof · cited by 13,712
CommSemiringproof · cited by 10,911
Top.topstatement and proof · cited by 9,680
CategoryTheory.Functor.mapstatement · cited by 8,698
SetLike.coestatement and proof · cited by 8,199
Set.Elemproof · cited by 7,166
CategoryTheory.Functor.compstatement · cited by 6,529

Cited by1

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AlgebraicGeometry.isIso_of_comp_eq_sigmaSpecproof · cited by 1