toAlternatingMap_injective — Mathlib

English

The range of toAlternatingMap consists exactly of those linear maps which are continuous.

Русский

Область значений toAlternatingMap состоит ровно из тех линейных отображений, которые непрерывны.

LaTeX

$$$\\operatorname{range}(\\mathrm{toAlternatingMap}) = \\{ f : M [⋀^ι]→ₗ[R] N \\,|\\, f \\text{ is continuous}\\}$$$

Lean4

theorem toAlternatingMap_injective : Injective (toAlternatingMap : (M [⋀^ι]→L[R] N) → (M [⋀^ι]→ₗ[R] N)) := fun f g h =>
  DFunLike.ext' <| by convert DFunLike.ext'_iff.1 h

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