∀ {E : Type u_2} {X : Type u_3} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} {I : Type u_1}
  [inst_2 : TopologicalSpace I] {x : X} (U : Set X) (hxU : x ∈ U) (H : ↑(f ⁻¹' U) ≃ₜ ↑U × I)
  (hH : ∀ (x : ↑(f ⁻¹' U)), ↑(H x).1 = f ↑x), Continuous fun i => ⟨↑(H.symm (⟨x, hxU⟩, i)), ⋯⟩