Theorems · Theorem · ring theory
IsDiscreteValuationRing.isOpen_iff
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : TopologicalSpace R] [IsTopologicalRing R] [CompactSpace R] [T2Space R]
[inst_5 : IsDomain R] [IsDiscreteValuationRing R] {I : Ideal R}, IsOpen ↑I ↔ I ≠ ⊥- Defined in
- Mathlib.Topology.Algebra.Ring.Compact
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CommRingstatement and proof · cited by 17,173
- SetLike.coestatement · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Bot.botstatement · cited by 4,720
- IsOpenstatement · cited by 2,400
- IsDomainstatement and proof · cited by 2,196
- T2Spacestatement and proof · cited by 1,351
- CompactSpacestatement and proof · cited by 593
- IsTopologicalRingstatement and proof · cited by 402
- IsDiscreteValuationRingstatement and proof · cited by 117
- IsDiscreteValuationRing.not_isFieldproof · cited by 2
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