instMulAction — Mathlib

English

As in 196851, a nontrivial normed module E over a nontrivial field 𝕜 is a perfect space.

Русский

Как и ранее, ненулевая норма над ненулевым полем образует совершенное пространство.

LaTeX

$$$\text{PerfectSpace } E$ for nontrivial normed field 𝕜 and module E over 𝕜.$$

Lean4

/-- If a monoid `M` distributively continuously acts on `𝕜` and this action commutes with
multiplication on `𝕜`, then it acts on `WeakDual 𝕜 E`. -/
instance instMulAction (M) [Monoid M] [DistribMulAction M 𝕜] [SMulCommClass 𝕜 M 𝕜] [ContinuousConstSMul M 𝕜] :
    MulAction M (WeakDual 𝕜 E) :=
  ContinuousLinearMap.mulAction

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