Theorems · Theorem · algebraic geometry
PrimeSpectrum.isTopologicalBasis_basic_opens
∀ {R : Type u} [inst : CommSemiring R],
TopologicalSpace.IsTopologicalBasis (Set.range fun r => ↑(PrimeSpectrum.basicOpen r))- Cited by
- 11 results in Mathlib
- Foundations
- Depth 81 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.
Cites22
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
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement and proof · cited by 8,199
- Set.rangestatement and proof · cited by 4,705
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- compl_complproof · cited by 229
- Set.singleton_subset_iffproof · cited by 206
- PrimeSpectrum.zeroLocusproof · cited by 164
Cited by11
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isBasis_basic_opensproof · cited by 16
- PrimeSpectrum.toPiLocalization_surjective_of_discreteTopologyproof · cited by 2
- PrimeSpectrum.isCompact_isOpen_iffproof · cited by 2
- PrimeSpectrum.exists_constructibleSetData_iffproof · cited by 2
- MvPolynomial.isOpenMap_comap_Cproof · cited by 1
- PrimeSpectrum.eq_biUnion_of_isOpenproof · cited by 1
- PrimeSpectrum.isHomeomorph_comapproof · cited by 1
- Polynomial.isOpenMap_comap_Cproof · cited by 0
- PrimeSpectrum.isOpenEmbedding_sigmaToPiproof · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.toΓSpec_continuousproof · cited by 0