Theorems · Theorem · algebraic geometry
PrimeSpectrum.basicOpen_one
∀ {R : Type u} [inst : CommSemiring R], PrimeSpectrum.basicOpen 1 = ⊤- Cited by
- 7 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Top.topstatement · cited by 9,680
- Set.univproof · cited by 3,945
- Compl.complproof · cited by 2,925
- TopologicalSpace.Opensstatement · cited by 2,040
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.basicOpenstatement · cited by 163
- TopologicalSpace.Opens.extproof · cited by 83
- PrimeSpectrum.basicOpen_eq_zeroLocus_complproof · cited by 34
- Set.compl_emptyproof · cited by 33
- PrimeSpectrum.zeroLocus_singleton_oneproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.smoothLocus_eq_univ_iffproof · cited by 3
- AlgebraicGeometry.Scheme.Modules.toOpen_fromTildeΓ_appproof · cited by 2
- AlgebraicGeometry.StructureSheaf.toOpenₗ_top_bijectiveproof · cited by 1
- AlgebraicGeometry.LocallyRingedSpace.Γ_Spec_left_triangleproof · cited by 1
- PrimeSpectrum.le_basicOpen_powproof · cited by 0
- AlgebraicGeometry.LocallyRingedSpace.toStalk_stalkMap_toΓSpecproof · cited by 0
- AlgebraicGeometry.StructureSheaf.const_oneproof · cited by 0