Theorems · Theorem · commutative algebra
IsValuativeTopology.mem_nhds_zero_iff
∀ {R : Type u_1} [inst : Ring R] [inst_1 : ValuativeRel R] [inst_2 : TopologicalSpace R] [IsValuativeTopology R]
(s : Set R), s ∈ nhds 0 ↔ ∃ γ, {x | (ValuativeRel.valuation R) x < ↑γ} ⊆ s- Cited by
- 0 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Ringstatement and proof · cited by 7,463
- Set.ofPredstatement and proof · cited by 6,101
- nhdsstatement · cited by 5,554
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- sub_zeroproof · cited by 938
- Valuationstatement · cited by 823
- ValuativeRelstatement and proof · cited by 241
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