Theorems · Theorem · algebraic geometry
PrimeSpectrum.discreteTopology_of_toLocalization_surjective
∀ {R : Type u} [inst : CommSemiring R],
Function.Surjective ⇑(PrimeSpectrum.toPiLocalization R) → DiscreteTopology (PrimeSpectrum R)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Idealproof · cited by 4,748
- AlgHomstatement · cited by 3,236
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement · cited by 625
- Ideal.primeComplstatement · cited by 462
- DiscreteTopologystatement · cited by 373
- PrimeSpectrum.asIdealstatement · cited by 333
- Localizationstatement · cited by 270
- PrimeSpectrum.PiLocalizationstatement · cited by 20
- PrimeSpectrum.toPiLocalizationstatement and proof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.discreteTopology_iff_toPiLocalization_surjectiveproof · cited by 1