Mathlib Map

Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.isBasis_affineOpens

∀ (X : AlgebraicGeometry.Scheme), TopologicalSpace.Opens.IsBasis X.affineOpens
Defined in
Mathlib.AlgebraicGeometry.AffineScheme
Cited by
37 results in Mathlib
Foundations
Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.iSup_affineOpens_eq_top · cited by 13AlgebraicGeometry.iSup_af…AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk · cited by 8Scheme.SpecMap_stalkMap_f…AlgebraicGeometry.Scheme.SpecMap_stalkSpecializes_fromSpecStalk · cited by 6Scheme.SpecMap_stalkSpeci…AlgebraicGeometry.isCompact_and_isOpen_iff_finite_and_eq_biUnion_affineOpens · cited by 4AlgebraicGeometry.isCompa…AlgebraicGeometry.Scheme.Hom.range_subset_ker_support · cited by 4Hom.range_subset_ker_supp…AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdeal · cited by 4IdealSheafData.le_support…AlgebraicGeometry.HasRingHomProperty.iff_exists_appLE_locally · cited by 3HasRingHomProperty.iff_ex…AlgebraicGeometry.Scheme.Spec_stalkClosedPointTo_fromSpecStalk · cited by 3Scheme.Spec_stalkClosedPo…AlgebraicGeometry.iSup_basicOpen_of_span_eq_top · cited by 2AlgebraicGeometry.iSup_ba…AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIso · cited by 2HasRingHomProperty.stalkM…AlgebraicGeometry.Scheme.fromSpecStalk_app · cited by 2Scheme.fromSpecStalk_appAlgebraicGeometry.exists_appTop_π_eq_of_isLimit · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.exists_smooth_of_formallySmooth_stalk · cited by 2AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.Hom.app_injective · cited by 1Hom.app_injectiveAlgebraicGeometry.Scheme.exists_isQuasiAffine_of_isLimit · cited by 1Scheme.exists_isQuasiAffi…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coeSet.ofPred · cited by 6101Set.ofPredSet.range · cited by 4705Set.rangeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.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.PresheafedSpace.Hom.base · cited by 1135Hom.baseScheme.isBasis_affineOpensCITED BYCITES

Cites29

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by37

Results whose statement or proof uses this declaration.