Theorems · Theorem · commutative algebra

Valued.discreteTopology_of_forall_map_eq_one

∀ {R : Type u} [inst : Ring R] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [_i : Valued R Γ₀],
  (∀ (x : R), x ≠ 0 → Valued.v x = 1) → DiscreteTopology R

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderedCommGroupWithZeroValued