fromInduced — Mathlib

English

Continuity of the induced maps X → induced f is ensured by the induced topology.

Русский

Непрерывность отображений из Induced обеспечена за счёт индуктивной топологии.

LaTeX

$$$\\forall i,\\; \\text{ContinuousAdd}((X_i).carrier) \\Rightarrow \\text{continuous}(f_i).$$$

Lean4

/-- The maps from the induced topology as homs in `TopModuleCat R`. -/
def fromInduced (i) : induced f ⟶ X i :=
  ofHom (X := induced f) ⟨(f i).hom, continuous_iff_le_induced.mpr (iInf_le _ i)⟩

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