toContinuousAffineMap — Mathlib

English

The contLinear part distributes over product: (f.prod g).contLinear = f.contLinear.prod g.contLinear.

Русский

Континуальная линейная часть распределяется по произведению: (f.prod g).contLinear = f.contLinear.prod g.contLinear.

LaTeX

$$$$(f.prod g).contLinear = f.contLinear.prod g.contLinear.$$$$

Lean4

/-- A continuous linear map can be regarded as a continuous affine map. -/
def toContinuousAffineMap (f : V →L[R] W) : V →ᴬ[R] W
    where
  toFun := f
  linear := f
  map_vadd' := by simp
  cont := f.cont

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