closure — Mathlib

English

If a set A of functions from β to α is uniformly equicontinuous, then its closure is uniformly equicontinuous.

Русский

Если множество функций A: β → α равномерно эконтинуально, то его замыкание равномерно эконтinuально.

LaTeX

$$$A\text{ UniformEquicontinuous} \Rightarrow \overline{A}\text{ UniformEquicontinuous}$$$

Lean4

/-- If a set of functions is uniformly equicontinuous, its closure for the product topology is also
uniformly equicontinuous. -/
protected theorem closure {A : Set <| β → α} (hA : A.UniformEquicontinuous) : (closure A).UniformEquicontinuous :=
  UniformEquicontinuous.closure' (u := id) hA continuous_id

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