continuousAlternatingMapCongr — Mathlib

English

Continuous linear equivalences commute with restrictScalars, giving a canonical equivalence.

Русский

Не прерывая ограничение скаляров, эквивалентности дают каноническое соответствие.

LaTeX

$$$\mathrm{restrictScalarsLI}$ is compatible with ContinuousLinearEquiv$$

Lean4

/-- Continuous linear equivalences between the domains and the codomains
generate a continuous linear equivalence between the spaces of continuous alternating maps. -/
@[simps! apply]
def continuousAlternatingMapCongr (e : E ≃L[𝕜] E') (e' : F ≃L[𝕜] F') : (E [⋀^ι]→L[𝕜] F) ≃L[𝕜] (E' [⋀^ι]→L[𝕜] F') :=
  e.continuousAlternatingMapCongrLeft.trans <| e'.continuousAlternatingMapCongrRight

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