disjoint_nhds_cobounded — Mathlib

English

For every x, the neighborhood filter at x is disjoint from the cobounded filter.

Русский

Для каждого x фильтр окрестностей точки x дисjoint от когобounded фильтра.

LaTeX

$$$\\\\forall x:\\\\alpha, \\\\ Disjoint(\\\\Nabla x, cobounded(\\\\alpha)).$$$

Lean4

theorem disjoint_nhds_cobounded (x : α) : Disjoint (𝓝 x) (cobounded α) :=
  disjoint_of_disjoint_of_mem disjoint_compl_right (ball_mem_nhds _ one_pos) isBounded_ball

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