instContinuousLinearMapClass — Mathlib

English

Elements of the character space act as continuous linear maps from A to 𝕜.

Русский

Элементы пространства характеров действуют как непрерывные линейные отображения от A к 𝕜.

LaTeX

$$$\\text{CharacterSpace}_{𝕜} A \\text{ consists of continuous linear maps } A \\to 𝕜.$$$

Lean4

/-- Elements of the character space are continuous linear maps. -/
instance instContinuousLinearMapClass : ContinuousLinearMapClass (characterSpace 𝕜 A) 𝕜 A 𝕜
    where
  map_smulₛₗ φ := (φ : WeakDual 𝕜 A).map_smul
  map_add φ := (φ : WeakDual 𝕜 A).map_add
  map_continuous φ := (φ : WeakDual 𝕜 A).cont

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