uniformContinuous — Mathlib

English

For any f in the CompactlySupportedContinuousMapClass F α β, the function f: β → γ is uniformly continuous (provided the relevant uniform structures exist).

Русский

Для любого элемента f в классе CompactlySupportedContinuousMap_Class F α β функция f: β → γ равна равномерно непрерывной (при наличии соответствующих структур единиц).

LaTeX

$$$$ \forall f,\ UniformContinuous( (f : β \to γ) ). $$$$

Lean4

theorem uniformContinuous (f : F) : UniformContinuous (f : β → γ) :=
  (map_continuous f).uniformContinuous_of_tendsto_cocompact (HasCompactSupport.is_zero_at_infty (hasCompactSupport f))

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