(** * 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_pt_ext_loc : forall f g x, locally x (fun x => f x = g x) -> continuity_pt f x -> continuity_pt g x.