Theorems · Theorem · commutative algebra

Valuation.hasBasis_nhds_zero

∀ {R : Type u_1} [inst : Ring R] [inst_1 : ValuativeRel R] {Γ₀ : Type u_3} [inst_2 : LinearOrderedCommGroupWithZero Γ₀]
  [inst_3 : TopologicalSpace R] (v : Valuation R Γ₀) [v.Compatible] [IsValuativeTopology R],
  (nhds 0).HasBasis (fun x => True) fun γ => {x | v.restrict x < ↑γ}

Defined in

Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingValuativeRelLinearOrderedCommGroupWithZeroTopologicalSpaceValuation.CompatibleIsValuativeTopology