(** * 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)).