(** * 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_neq_0 :
forall f x y,
continuity_2d_pt f x y -> f x y <> 0 ->
locally_2d (fun u v => f u v <> 0) x y.