compl_mem_sets — Mathlib

English

For all a ∈ α, stoneCechExtend hg (stoneCechUnit a) = g a.

Русский

Для каждого a ∈ α, stoneCechExtend hg (stoneCechUnit a) = g a.

LaTeX

$$$ \forall a:\alpha, stoneCechExtend hg (stoneCechUnit a) = g a $$$

Lean4

/-- The complement to a compact set belongs to a filter `f` if it belongs to each filter
`𝓝 x ⊓ f`, `x ∈ s`. -/
theorem compl_mem_sets (hs : IsCompact s) {f : Filter X} (hf : ∀ x ∈ s, sᶜ ∈ 𝓝 x ⊓ f) : sᶜ ∈ f :=
  by
  contrapose! hf
  simp only [notMem_iff_inf_principal_compl, compl_compl, inf_assoc] at hf ⊢
  exact @hs _ hf inf_le_right

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