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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsAffineOpen.iSup_of_disjoint

∀ {σ : Type v} {X : AlgebraicGeometry.Scheme} [Finite σ] {U : σ → X.Opens},
  (∀ (i : σ), AlgebraicGeometry.IsAffineOpen (U i)) →
    Pairwise (Function.onFun Disjoint U) → AlgebraicGeometry.IsAffineOpen (iSup U)
Defined in
Mathlib.AlgebraicGeometry.Limits
Cited by
2 results in Mathlib
Foundations
Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Finite
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.IsAffineOpen.sup_of_disjoint · cited by 0IsAffineOpen.sup_of_disjo…AlgebraicGeometry.IsAffineOpen.biSup_of_disjoint · cited by 0IsAffineOpen.biSup_of_dis…DFunLike.coe · cited by 62936DFunLike.coeEquiv · cited by 8337EquivEquiv.symm · cited by 3681Equiv.symmTopCat.carrier · cited by 3184TopCat.carrierFinite · cited by 3029FiniteAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeiSup · cited by 2415iSupCommRingCat · cited by 2333CommRingCatDisjoint · cited by 2201DisjointAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensFunction.onFun · cited by 570Function.onFunIsAffineOpen.iSup_of_disjointCITED BYCITES

Cites21

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Cited by2

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