toContinuousMap — Mathlib

English

From a bundled morphism F with a ContinuousMapClass structure, one can form its underlying continuous map by pairing f with a proof of continuity: toContinuousMap(f) = ⟨f, map_continuous f⟩.

Русский

Из связанного морфизма F с структурой ContinuousMapClass можно построить его базовую непрерывную карту, объединив функцию f и доказательство непрерывности: toContinuousMap(f) = ⟨f, map_continuous f⟩.

LaTeX

$$$toContinuousMap(f) = \\langle f,\\; map\\_continuous(f) \\rangle \\in C(X,Y)$$$

Lean4

/-- Coerce a bundled morphism with a `ContinuousMapClass` instance to a `ContinuousMap`. -/
@[coe]
def toContinuousMap (f : F) : C(X, Y) :=
  ⟨f, map_continuous f⟩

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