instIsUniformAddGroup — Mathlib

English

The space of continuous multilinear maps carries a natural topology defined as induced from UniformOnFun via toUniformOnFun.

Русский

Пространство непрерывных мультилінійних отображений имеет естественную топологию, получаемую как индуцированную от UniformOnFun через toUniformOnFun.

LaTeX

$$$[\text{TopologicalSpace} (\text{ContinuousMultilinearMap } 𝕜 E F)] = \text{induced} (\text{toUniformOnFun}, \text{UniformOnFun.topologicalSpace})$$$

Lean4

instance instIsUniformAddGroup : IsUniformAddGroup (ContinuousMultilinearMap 𝕜 E F) :=
  let φ : ContinuousMultilinearMap 𝕜 E F →+ (Π i, E i) →ᵤ[{s | IsVonNBounded 𝕜 s}] F :=
    { toFun := toUniformOnFun, map_add' := fun _ _ ↦ rfl, map_zero' := rfl }
  isUniformEmbedding_toUniformOnFun.isUniformAddGroup φ

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