Theorems · Theorem · commutative algebra

Valued.isClopen_ball

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

An open ball centred at the origin in a valued ring is clopen.

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingLinearOrderedCommGroupWithZeroValued