Additive characters of topological monoids

theorem DenseRange.addChar_eq_of_eval_one_eq {A : Type u_1} {M : Type u_2} [TopologicalSpace A] [AddMonoidWithOne A] [Monoid M] [TopologicalSpace M] [T2Space M] (hdr : DenseRange Nat.cast) {κ₁ κ₂ : AddChar A M} (hκ₁ : Continuous ⇑κ₁) (hκ₂ : Continuous ⇑κ₂) (h : κ₁ 1 = κ₂ 1) : κ₁ = κ₂