∀ {α : Type u_1} {β : Type u_2} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {ι : Type u_3}
  {U : ι → TopologicalSpace.Opens β},
  TopologicalSpace.IsOpenCover U →
    Continuous f → (Topology.IsOpenEmbedding f ↔ ∀ (i : ι), Topology.IsOpenEmbedding ((U i).carrier.restrictPreimage f))