disjoint_nhdsSet_right — Mathlib

English

A filter l is disjoint with nhdsSet s iff it is disjoint with nhds x for every x ∈ s.

Русский

Фильтр l дисjoint с nhdsSet s тогда и только тогда, когда он дисjoint с nhds x для каждой x ∈ s.

LaTeX

$$$Disjoint l (𝓝ˢ s) \leftrightarrow \forall x \in s, Disjoint l (𝓝 x)$$$

Lean4

/-- A filter `l` is disjoint with the neighborhood filter of a compact set if and only if it is
disjoint with the neighborhood filter of each point of this set. -/
theorem disjoint_nhdsSet_right {l : Filter X} (hs : IsCompact s) : Disjoint l (𝓝ˢ s) ↔ ∀ x ∈ s, Disjoint l (𝓝 x) := by
  simpa only [disjoint_comm] using hs.disjoint_nhdsSet_left

Похожие утверждения