Theorems · Theorem · general topology

IsProperMap.prodMap

∀ {X : Type u_1} {Y : Type u_2} {Z : Type u_3} {W : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] {f : X → Y} {g : Z → W},
  IsProperMap f → IsProperMap g → IsProperMap (Prod.map f g)

A binary product of proper maps is proper.

Defined in

Mathlib.Topology.Maps.Proper.Basic

Cited by

7 results in Mathlib

Foundations

Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpace