(** * 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_filterlim :
forall f x y,
continuity_2d_pt f x y <->
filterlim (fun z : R * R => f (fst z) (snd z)) (locally (x,y)) (locally (f x y)).