Theorems · Theorem · commutative algebra

Valued.mem_nhds

∀ {R : Type u} [inst : Ring R] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [_i : Valued R Γ₀] {s : Set R}
  {x : R}, s ∈ nhds x ↔ ∃ γ, {y | Valued.v.restrict (y - x) < ↑γ} ⊆ s

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

7 results in Mathlib

Foundations

Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderedCommGroupWithZeroValued