Theorems · Theorem · algebraic geometry
PrimeSpectrum.isBasis_basic_opens
∀ {R : Type u} [inst : CommSemiring R], TopologicalSpace.Opens.IsBasis (Set.range PrimeSpectrum.basicOpen)- Cited by
- 16 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpaceproof · cited by 24,529
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.rangestatement and proof · cited by 4,705
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement and proof · cited by 625
- Set.range_compproof · cited by 223
- PrimeSpectrum.basicOpenstatement and proof · cited by 163
- TopologicalSpace.IsTopologicalBasisproof · cited by 126
- TopologicalSpace.Opens.IsBasisstatement · cited by 30
Cited by16
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isBasis_basicOpenproof · cited by 3
- AlgebraicGeometry.Scheme.IsQuasiAffine.isBasis_basicOpenproof · cited by 2
- AlgebraicGeometry.Scheme.exists_affine_mem_range_and_range_subsetproof · cited by 2
- PrimeSpectrum.isOpenMap_comap_of_hasGoingDown_of_finitePresentationproof · cited by 2
- Algebra.IsSmoothAt.exists_notMem_smoothproof · cited by 2
- AlgebraicGeometry.Scheme.affineBasisCover_is_basisproof · cited by 2
- Algebra.isOpen_smoothLocusproof · cited by 2
- Algebra.exists_formallyUnramified_of_isUnramifiedAtproof · cited by 2
- Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐproof · cited by 1
- AlgebraicGeometry.compactSpace_of_universallyClosedproof · cited by 1
- AlgebraicGeometry.Spec.basicOpen_hom_extproof · cited by 1
- Algebra.exists_etale_of_isEtaleAtproof · cited by 1