Theorems · Theorem · algebraic geometry
PrimeSpectrum.discreteTopology_iff_toPiLocalization_bijective
∀ {R : Type u_1} [inst : CommSemiring R],
DiscreteTopology (PrimeSpectrum R) ↔ Function.Bijective ⇑(PrimeSpectrum.toPiLocalization R)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- AlgHomstatement · cited by 3,236
- Function.Bijectivestatement · cited by 863
- 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 · cited by 13
- PrimeSpectrum.toPiLocalization_injectiveproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Module.Finite.of_quasiFiniteproof · cited by 7
- PrimeSpectrum.toPiLocalization_bijectiveproof · cited by 1