Theorems · Theorem · general topology

IsOpenMap.of_comp

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

If g ∘ f is open, where f is continuous and surjective, then g is open.

Defined in

Mathlib.Topology.Maps.Basic

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpace