Theorems · Theorem · commutative algebra
Valuation.discreteTopology_of_forall_lt
∀ {K : Type u_2} [inst : DivisionRing K] [inst_1 : ValuativeRel K] {Γ₀ : Type u_3}
[inst_2 : LinearOrderedCommGroupWithZero Γ₀] [inst_3 : TopologicalSpace K] [IsValuativeTopology K] [MulArchimedean Γ₀]
(v : Valuation K Γ₀) [v.Compatible] {r : Γ₀}, r ≠ 0 → (∀ (x : K), v x ≠ 0 → r < v x) → DiscreteTopology K- Cited by
- 0 results in Mathlib
- Foundations
- Depth 103 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.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement and proof · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- DiscreteTopologystatement · cited by 373
- ValuativeRelstatement and proof · cited by 241
- Valuation.Compatiblestatement and proof · cited by 71
- IsValuativeTopologystatement and proof · cited by 47
- MulArchimedeanstatement and proof · cited by 45
- Valuation.map_eq_one_of_forall_ltproof · cited by 2
- Valuation.discreteTopology_of_forall_map_eq_oneproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.