Theorems · Theorem · general topology

isProperMap_of_comp_of_t2

∀ {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} [T2Space Y],
  Continuous f → Continuous g → IsProperMap (g ∘ f) → IsProperMap f

If the composition of two continuous functions f : X → Y and g : Y → Z is proper and Y is T2, then f is proper.

Defined in

Mathlib.Topology.Maps.Proper.Basic

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceT2Space