prod_nhds_le_of_disjoint_cocompact

English

Let f : Filter X and t ⊆ Y be such that t is compact and f is disjoint from cocompact Y. Then f ×ˢ 𝓝 y ≤ 𝓝ˢ (Set.univ ×ˢ t).

Русский

Пусть f — фильтр на X и t ⊆ Y компактно; f дисjoint с cocompact Y. Тогда f ×ˢ 𝓝ˢ t ≤ 𝓝ˢ (Set.univ ×ˢ t).

LaTeX

$$$ f \timesˢ 𝓝ˢ t \le 𝓝ˢ (Set.univ \timesˢ t)$$$

Lean4

theorem prod_nhds_le_of_disjoint_cocompact {f : Filter X} (y : Y) (hf : Disjoint f (Filter.cocompact X)) :
    f ×ˢ 𝓝 y ≤ 𝓝ˢ (Set.univ ×ˢ { y }) := by simpa using prod_nhdsSet_le_of_disjoint_cocompact isCompact_singleton hf

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