instModule — Mathlib

English

Under surjectivity and isometry hypotheses on σ, the multiplication by scalars on UniformConvergenceCLM σ F 𝔖 is continuous.

Русский

При условиях surjective и изометрии на σ непрерывно равно скалярное умножение на UniformConvergenceCLM σ F 𝔖.

LaTeX

$$$\\text{ContinuousSMul } 𝕜_2 (\\mathrm{UniformConvergenceCLM}(\\sigma,F,\\mathcal{S}))$$$

Lean4

instance instModule (R : Type*) [Semiring R] [Module R F] [SMulCommClass 𝕜₂ R F] [TopologicalSpace F]
    [ContinuousConstSMul R F] [IsTopologicalAddGroup F] (𝔖 : Set (Set E)) : Module R (UniformConvergenceCLM σ F 𝔖) :=
  ContinuousLinearMap.module

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