Theorems · Theorem · commutative algebra
Valued.discreteTopology_of_forall_lt
∀ {K : Type u} [inst : DivisionRing K] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [MulArchimedean Γ₀]
[inst_3 : Valued K Γ₀] {r : Γ₀}, r ≠ 0 → (∀ (x : K), Valued.v x ≠ 0 → r < Valued.v x) → DiscreteTopology K- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- DivisionRingstatement and proof · cited by 1,062
- Valuationstatement · cited by 823
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- DiscreteTopologystatement · cited by 373
- Valued.vstatement and proof · cited by 163
- Valuedstatement and proof · cited by 70
- MulArchimedeanstatement and proof · cited by 45
- Valuation.map_eq_one_of_forall_ltproof · cited by 2
- Valued.discreteTopology_of_forall_map_eq_oneproof · cited by 1
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.