uniformContinuousConstSMul — Mathlib

English

Uniform embedding result for the map to UniformOnFun representation is preserved under the UniformOnFun structure.

Русский

Результат uniform embedding для отображения к представлению UniformOnFun сохраняется при структуре UniformOnFun.

LaTeX

$$$$ IsUniformEmbedding (f \mapsto UniformOnFun.ofFun \{s| Bornology.IsVonNBounded 𝕜₁ s\} f) \left( ContinuousLinearMap.funLike.coe f \right) $$$$

Lean4

instance uniformContinuousConstSMul {M : Type*} [Monoid M] [DistribMulAction M F] [SMulCommClass 𝕜₂ M F]
    [UniformSpace F] [IsUniformAddGroup F] [UniformContinuousConstSMul M F] :
    UniformContinuousConstSMul M (E →SL[σ] F) :=
  UniformConvergenceCLM.instUniformContinuousConstSMul σ F _ _

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