uniformity_hasBasis_closure — Mathlib

English

The family of closed entourages forms a basis of the uniformity: HasBasis (𝓤 α) (fun V : Set (α × α) => V ∈ 𝓤 α) closure.

Русский

Семейство замкнутых энтурджей образует базис униформности: HasBasis (𝓤 α) (fun V : Set (α × α) => V ∈ 𝓤 α) closure.

LaTeX

$$$HasBasis (\\mathcal{U} α) (\\lambda V : \\mathrm{Set}(α \\times α) \\Rightarrow V \\in \\mathcal{U} α) \\mathrm{closure}$$$

Lean4

/-- Closed entourages form a basis of the uniformity filter. -/
theorem uniformity_hasBasis_closure : HasBasis (𝓤 α) (fun V : Set (α × α) => V ∈ 𝓤 α) closure :=
  (𝓤 α).basis_sets.uniformity_closure

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