Equicontinuous — Mathlib

English

EquicontinuousWithinAt is equivalent to the stated universal property with nhdsWithin, i.e., an equivalence with nhdsWithin x0 on S.

Русский

EquicontinuousWithinAt эквивалентно свойству существования окружения nhdsWithin x0 на S.

LaTeX

$$$EquicontinuousWithinAt(F,S,x_0) \iff (∀ U ∈ 𝓤(α), U\text{–покрытие}, 𝓕)$. (formal equivalence with nhdsWithin)$$

Lean4

/-- A family `F : ι → X → α` of functions from a topological space to a uniform space is
*equicontinuous* on all of `X` if it is equicontinuous at each point of `X`. -/
def Equicontinuous (F : ι → X → α) : Prop :=
  ∀ x₀, EquicontinuousAt F x₀

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