instContinuousConstSMul — Mathlib

English

Reiterates the R-module structure on WeakDual under scalar actions and IsScalarTower relations.

Русский

Повторение структуры модуля над R для WeakDual при условиях скаляров и IsScalarTower.

LaTeX

$$$\text{WeakDual.instModule' }(R)\;\text{module}$$$

Lean4

instance instContinuousConstSMul (M) [Monoid M] [DistribMulAction M 𝕜] [SMulCommClass 𝕜 M 𝕜] [ContinuousConstSMul M 𝕜] :
    ContinuousConstSMul M (WeakDual 𝕜 E) :=
  ⟨fun m => continuous_induced_rng.2 <| (WeakBilin.coeFn_continuous (topDualPairing 𝕜 E)).const_smul m⟩

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