(** * 2D-continuity *)

(** ** Definitions *)

Definition continuity_2d_pt f x y :=
  forall eps : posreal, locally_2d (fun u v => Rabs (f u v - f x y) < eps) x y.

Lemma continuity_2d_pt_plus (f g : R -> R -> R) (x y : R) : continuity_2d_pt f x y -> continuity_2d_pt g x y -> continuity_2d_pt (fun u v => f u v + g u v) x y.