∀ {E : Type u_1} {X : Type u_2} [inst : TopologicalSpace E] [inst_1 : TopologicalSpace X] {f : E → X} {I : Type u_3}
  [inst_2 : TopologicalSpace I] {x : X},
  IsEvenlyCovered f x I → ∀ {Y : Type u_4} [inst_3 : TopologicalSpace Y] (g : X ≃ₜ Y), IsEvenlyCovered (⇑g ∘ f) (g x) I