compLeftContinuous — Mathlib

English

The constant map x ↦ m defines a ContinuousLinearMap from the ground ring R to C(α, M).

Русский

Постоянное отображение x ↦ m задаёт непрерывный линейный отображатель от R к C(α, M).

LaTeX

$$$\text{const}_{\alpha}(m): R \to L[R] C(α, M).$$$

Lean4

/-- Composition on the left by a continuous linear map, as a `ContinuousLinearMap`.
Similar to `LinearMap.compLeft`. -/
@[simps]
protected def _root_.ContinuousLinearMap.compLeftContinuous (α : Type*) [TopologicalSpace α] (g : M →L[R] M₂) :
    C(α, M) →L[R] C(α, M₂)
    where
  __ := g.toLinearMap.toAddMonoidHom.compLeftContinuous α g.continuous
  map_smul' := fun c _ => ext fun _ => g.map_smul' c _
  cont := ContinuousMap.continuous_postcomp _

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