Theorems · Theorem · general topology

isProperMap_of_comp_of_surj

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] {f : X → Y} {g : Y → Z},
  Continuous f → Continuous g → IsProperMap (g ∘ f) → Function.Surjective f → IsProperMap g

If the composition of two continuous functions g ∘ f is proper and f is surjective, then g is proper.

Defined in

Mathlib.Topology.Maps.Proper.Basic

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace