Theorems · Theorem · algebraic geometry
IsLocalRing.closedPoint_mem_iff
∀ {R : Type u} [inst : CommSemiring R] [inst_1 : IsLocalRing R] (U : TopologicalSpace.Opens (PrimeSpectrum R)),
IsLocalRing.closedPoint R ∈ U ↔ U = ⊤- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringIsLocalRing
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 and proof · cited by 9,680
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- PrimeSpectrumstatement and proof · cited by 625
- IsLocalRingstatement and proof · cited by 339
- eq_top_iffproof · cited by 236
- TopologicalSpace.Opens.is_open'proof · cited by 139
- IsLocalRing.closedPointstatement and proof · cited by 60
- Specializes.mem_openproof · cited by 27
- IsLocalRing.specializes_closedPointproof · cited by 6
- TopologicalSpace.Opens.mem_topproof · cited by 4
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