Theorems · Theorem · commutative algebra

Valued.cauchy_iff

∀ {R : Type u} [inst : Ring R] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [_i : Valued R Γ₀]
  {F : Filter R},
  Cauchy F ↔
    F.NeBot ∧
      ∀ (γ : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀ˣ),
        ∃ M ∈ F, ∀ x ∈ M, ∀ y ∈ M, Valued.v.restrict (y - x) < ↑γ

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

0 results in Mathlib

Foundations

Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderedCommGroupWithZeroValued