isUniformEmbedding_toContinuousMultilinearMap

English

The map toContinuousMultilinearMap is an isUniformEmbedding; hence it is injective and preserves uniform structure up to the natural identification.

Русский

Отображение toContinuousMultilinearMap является изUniformEmbedding; следовательно, оно инъективно и сохраняет униформную структуру в естественном тождественном виде.

LaTeX

$$$$ IsUniformEmbedding (toContinuousMultilinearMap) $$$$

Lean4

theorem isUniformEmbedding_toContinuousMultilinearMap :
    IsUniformEmbedding (toContinuousMultilinearMap : (E [⋀^ι]→L[𝕜] F) → _)
    where
  injective := toContinuousMultilinearMap_injective
  comap_uniformity := rfl

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