deltaGenerated_eq_coinduced — Mathlib

English

For a given X, the delta-generated topology equals the coinduced topology via a single canonical map when viewed through the sigma-construction.

Русский

Для данного X дельта-генерированная топология равна когенерированной топологии через единственную каноническую карту в сигм-структуре.

LaTeX

$$$\\DeltaGeneratedSpace(X) \\;=\\; \\text{coinduced}(\\text{canonical map}, t_X)$$$

Lean4

/-- The delta-generated topology is also coinduced by a single map out of a sigma type. -/
theorem deltaGenerated_eq_coinduced :
    deltaGenerated X = coinduced (fun x : (f : (n : ℕ) × C(Fin n → ℝ, X)) × (Fin f.1 → ℝ) ↦ x.1.2 x.2) inferInstance :=
  by rw [deltaGenerated, instTopologicalSpaceSigma, coinduced_iSup]; rfl

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