closure — Mathlib

English

If a set A of functions from X to α is equicontinuous (in the product topology), then its closure in the same space is also equicontinuous.

Русский

Если множество функций A: X → α экконтинуально (в произведённой топологии), то его замыкание в той же пространства экконтинуально.

LaTeX

$$$A\ \text{то } A\text{ Equicontinuous} \Rightarrow \overline{A}\ \text{Equicontinuous}$$$

Lean4

/-- If a set of functions is equicontinuous, its closure for the product topology is also
equicontinuous. -/
protected theorem closure {A : Set <| X → α} (hA : A.Equicontinuous) : (closure A).Equicontinuous := fun x ↦
  Set.EquicontinuousAt.closure (hA x)

Похожие утверждения