restrictScalarsLinear — Mathlib

English

If F is T2, then CM_k(E,F) is T3 as an instance.

Русский

Если F T2, CM_k(E,F) — T3 как инстанс.

LaTeX

$$$[T2Space F] \\Rightarrow T3Space (\\mathrm{CM}_k(E,F))$$$

Lean4

/-- `ContinuousMultilinearMap.restrictScalars` as a `ContinuousLinearMap`. -/
@[simps -fullyApplied apply]
def restrictScalarsLinear [ContinuousConstSMul 𝕜' F] :
    ContinuousMultilinearMap 𝕜 E F →L[𝕜'] ContinuousMultilinearMap 𝕜' E F
    where
  toFun := restrictScalars 𝕜'
  map_add' _ _ := rfl
  map_smul' _ _ := rfl

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