Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.isDiscrete_comap_preimage_singleton
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
[Algebra.QuasiFinite R S] (P : PrimeSpectrum R), IsDiscrete (PrimeSpectrum.comap (algebraMap R S) ⁻¹' {P})- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.preimagestatement · cited by 4,946
- Algebra.algebraMapstatement · cited by 4,706
- PrimeSpectrumstatement and proof · cited by 625
- Homeomorph.symmproof · cited by 365
- PrimeSpectrum.comapstatement · cited by 199
- IsDiscretestatement · cited by 86
- Algebra.QuasiFinitestatement and proof · cited by 28
- PrimeSpectrum.preimageHomeomorphFiberproof · cited by 6
- Homeomorph.discreteTopologyproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.QuasiFinite.eq_of_le_of_under_eqproof · cited by 1
- Algebra.QuasiFinite.isDiscrete_comap_preimageproof · cited by 1