Theorems · Theorem · commutative algebra

Valued.isClopen_sphere

∀ (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 sphere centred at the origin in a valued ring is clopen.

Defined in

Mathlib.Topology.Algebra.Valued.ValuationTopology

Cited by

2 results in Mathlib

Foundations

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

Assumes

RingLinearOrderedCommGroupWithZeroValued