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]