Theorems · Theorem · commutative algebra

Valuation.hasBasis_uniformity

∀ {R : Type u_1} [inst : Ring R] [inst_1 : ValuativeRel R] {Γ₀ : Type u_3} [inst_2 : LinearOrderedCommGroupWithZero Γ₀]
  [_u : UniformSpace R] [IsUniformAddGroup R] [IsValuativeTopology R] (v : Valuation R Γ₀) [v.Compatible],
  (uniformity R).HasBasis (fun x => True) fun γ => {p | v.restrict (p.2 - p.1) < ↑γ}

Defined in

Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingValuativeRelLinearOrderedCommGroupWithZeroUniformSpaceIsUniformAddGroupIsValuativeTopologyValuation.Compatible