continuousConstSMul_rat — Mathlib

English

The rational scalar action on a division ring with topology is continuous.

Русский

Рациональная скалярная параллельная деформация на делении кольца с топологией непрерывна.

LaTeX

$$$\text{ContinuousConstSMul}_{\mathbb{Q}}(A)$$$

Lean4

/-- The action induced by `DivisionRing.toRatAlgebra` is continuous. -/
instance continuousConstSMul_rat {A} [DivisionRing A] [TopologicalSpace A] [ContinuousMul A] [CharZero A] :
    ContinuousConstSMul ℚ A :=
  ⟨fun r => by simpa only [Algebra.smul_def] using continuous_const.mul continuous_id⟩

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