rangeFactorization — Mathlib

English

If f is continuous, then the range factorization map is continuous; conversely, a supplement. (Standard equivalence stated in theorems.)

Русский

Если f непрерывно, то диапазонное разложение непрерывно; эквивалентность выражена в теоремах.

LaTeX

$$$\text{Continuous}(\text{rangeFactorization } f) \iff \text{Continuous}(f).$$$

Lean4

@[continuity, fun_prop]
theorem rangeFactorization {f : X → Y} (hf : Continuous f) : Continuous (rangeFactorization f) :=
  continuous_rangeFactorization_iff.mpr hf

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