uniformity_hasBasis_open — Mathlib

English

Open elements of 𝓤 α form a basis of 𝓤 α: HasBasis (𝓤 α) (fun V : Set (α × α) => V ∈ 𝓤 α ∧ IsOpen V) id.

Русский

Открытые элементы 𝓤 α образуют базис аль 𝓤 α: HasBasis (𝓤 α) (fun V : Set (α × α) => V ∈ 𝓤 α ∧ IsOpen V) id.

LaTeX

$$$HasBasis (\\mathcal{U} α) (\\lambda V : \\mathrm{Set}(α \\times α) => V ∈ \\mathcal{U} α ∧ \\mathrm{IsOpen} V) id$$$

Lean4

/-- Open elements of `𝓤 α` form a basis of `𝓤 α`. -/
theorem uniformity_hasBasis_open : HasBasis (𝓤 α) (fun V : Set (α × α) => V ∈ 𝓤 α ∧ IsOpen V) id :=
  hasBasis_self.2 fun s hs => ⟨interior s, interior_mem_uniformity hs, isOpen_interior, interior_subset⟩

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