(** * 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_ext_loc : forall f g x y, locally_2d (fun u v => f u v = g u v) x y -> continuity_2d_pt f x y -> continuity_2d_pt g x y.