nhds_atTop — Mathlib

English

If α is a preorder, the neighborhood of atTop is the infimum over x of principal filters of Iic(Ici x).

Русский

Если α—предобозначение, окрестности atTop равны пересечению по x базиса из 𝓟(Iic(𝓟(Ici x))).

LaTeX

$$$𝓝(\text{atTop}) = \bigwedge_{x \in α} \mathcal{P}\big( \mathrm{Iic}(\mathcal{P}(\mathrm{Ici} x)) \big).$$$

Lean4

theorem nhds_atTop [Preorder α] : 𝓝 atTop = ⨅ x : α, 𝓟 (Iic (𝓟 (Ici x))) := by
  simp only [atTop, Filter.nhds_iInf, nhds_principal]

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