add_compContinuous — Mathlib

English

Equality of two left-composition constructions with Lipschitz maps holds on bounded continuous functions: comp with g hg preserves multiplication etc.

Русский

Справедливость двух левых композиционных конструирований с Lipschitz-картами на ограниченных непрерывных функциях: композиция сохраняет умножение и единицу.

LaTeX

$$$\text{compLeftContinuousBounded}(g, hg)$ preserves monoid structure; equality of maps on generators$$

Lean4

theorem add_compContinuous [Add β] [BoundedAdd β] [ContinuousAdd β] [TopologicalSpace γ] (f g : α →ᵇ β) (h : C(γ, α)) :
    (g + f).compContinuous h = g.compContinuous h + f.compContinuous h :=
  rfl

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