Theorems · Theorem · commutative algebra

Valued.isClopen_closedBall

∀ (R : Type u) [inst : Ring R] {Γ₀ : Type v} [inst_1 : LinearOrderedCommGroupWithZero Γ₀] [_i : Valued R Γ₀]
  {r : (MonoidWithZeroHom.ofClass Valued.v).ValueGroup₀}, r ≠ 0 → IsClopen {x | Valued.v.restrict x ≤ r}

A closed ball centred at the origin in a valued ring is clopen.

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

3 results in Mathlib

Foundations

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

Assumes

RingLinearOrderedCommGroupWithZeroValued