Theorems · Theorem · commutative algebra

Valuation.mem_nhds_iff

∀ {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] {s : Set R} {x : R},
  s ∈ nhds x ↔ ∃ γ, {z | v.restrict (z - x) < ↑γ} ⊆ s

Defined in

Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology

Cited by

6 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingValuativeRelLinearOrderedCommGroupWithZeroTopologicalSpaceValuation.CompatibleIsValuativeTopology