continuous_quot_lift — Mathlib

English

Let X be a topological space, r a relation, and f: X → Y a map constant on r-equivalence classes. Then the lift to the quotient Quot r → Y is continuous.

Русский

Пусть X — топологическое пространство, r — эквивалентность, и f: X → Y such that f(a) = f(b) whenever a ~ b. Тогда отображение Quotient r → Y, заданное подъемом, непрерывно.

LaTeX

$$$$ \mathrm{Continuous}(\operatorname{Quotient\_lift}(f, hr)) $$$$

Lean4

@[continuity, fun_prop]
theorem continuous_quot_lift {f : X → Y} (hr : ∀ a b, r a b → f a = f b) (h : Continuous f) :
    Continuous (Quot.lift f hr : Quot r → Y) :=
  continuous_coinduced_dom.2 h

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