tendsto_nhds_left — Mathlib

English

Similarly, Tendsto u f (𝓝 a) is equivalent to Tendsto (λ x, (u x, a)) f (𝓤 α).

Русский

Аналогично, Tendsto u f (\\mathcal{N}(a)) эквивалентно Tendsto (λ x, (u x, a)) f (\\mathcal{U}(α)).

LaTeX

$$$\\operatorname{Tendsto}(u\\,f\, (\\mathcal{N}(a))) \\iff \\operatorname{Tendsto}(\\lambda x. (u x, a))\,f\, (\\mathcal{U}(\\alpha))$$$

Lean4

theorem tendsto_nhds_left {f : Filter β} {u : β → α} {a : α} :
    Tendsto u f (𝓝 a) ↔ Tendsto (fun x => (u x, a)) f (𝓤 α) := by rw [nhds_eq_comap_uniformity', tendsto_comap_iff]; rfl

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