∀ {G : Type u} [inst : TopologicalSpace G] {H : Type v} [inst_1 : TopologicalSpace H] [inst_2 : Add G] [inst_3 : Add H]
  (e : G ≃+ H) (he : ∀ (s : Set H), IsOpen (⇑e ⁻¹' s) ↔ IsOpen s) (a : G), (e.toContinuousAddEquiv he) a = e a