(** * Topology on [R]² *)
Definition locally_2d (P : R -> R -> Prop) x y :=
exists delta : posreal, forall u v, Rabs (u - x) < delta -> Rabs (v - y) < delta -> P u v.

Lemma locally_2d_locally :
forall P x y,
locally_2d P x y <-> locally (x,y) (fun z => P (fst z) (snd z)).