Theorems · Definition · functional analysis

continuousMultilinearCurryFin1

(𝕜 : Type u) →
  (G : Type wG) →
    (G' : Type wG') →
      [inst : NontriviallyNormedField 𝕜] →
        [inst_1 : NormedAddCommGroup G] →
          [inst_2 : NormedSpace 𝕜 G] →
            [inst_3 : NormedAddCommGroup G'] → [inst_4 : NormedSpace 𝕜 G'] → (G [×1]→L[𝕜] G') ≃ₗᵢ[𝕜] G →L[𝕜] G'

Continuous multilinear maps from G^1 to G' are isomorphic with continuous linear maps from G to G'.

Defined in

Mathlib.Analysis.Normed.Module.Multilinear.Curry

Cited by

58 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace