English
The quotient of the ker f by a surjective quotient map gives a homeomorphism to the codomain Y; Setoid.quotientKerEquivOfSurjective furnishes the underlying equivalence.
Русский
Квотирование ядра множества по сюръективному отображению образует гомеоморфизм к ко́дюнату Y; отображение задаётся через эквивалентность.
LaTeX
$$$\\text{homeomorph}(hf) : Quotient(\\ker f) \\cong_t Y$$$
Lean4
/-- `Setoid.quotientKerEquivOfRightInverse` as a homeomorphism. -/
@[simps!]
def homeomorph {f' : C(Y, X)} (hf : Function.RightInverse f' f) : Quotient (Setoid.ker f) ≃ₜ Y
where
toEquiv := Setoid.quotientKerEquivOfRightInverse _ _ hf
continuous_toFun := isQuotientMap_quot_mk.continuous_iff.mpr (map_continuous f)
continuous_invFun := continuous_quotient_mk'.comp (map_continuous f')
