equicontinuous_iInf_dom — Mathlib

English

If hk is Equicontinuous at each t k, then Equicontinuous at the infimum t.

Русский

Если эконтинуированность на каждом t_k, то на infimum выпадает.

LaTeX

$$$\\operatorname{Equicontinuous} F \\Rightarrow \\operatorname{Equicontinuous} F$ (under iInf of t_k).$$

Lean4

theorem equicontinuous_iInf_dom {t : κ → TopologicalSpace X'} {F : ι → X' → α} {k : κ}
    (hk : Equicontinuous (tX := t k) F) : Equicontinuous (tX := ⨅ k, t k) F := fun x ↦ equicontinuousAt_iInf_dom (hk x)

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