Theorems · Theorem · general topology

isOpenMap_prodMap_iff

∀ {X : Type u} {Y : Type v} {W : Type u_1} {Z : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y]
  [inst_2 : TopologicalSpace Z] [inst_3 : TopologicalSpace W] [Nonempty X] [Nonempty Z] {f : X → Y} {g : Z → W},
  IsOpenMap (Prod.map f g) ↔ IsOpenMap f ∧ IsOpenMap g

Defined in

Mathlib.Topology.Constructions.SumProd

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceNonemptyNonempty