End NVS_continuity.

(* Specifications: *)
Lemma filterlim_mult {K : AbsRing} (x y : K) :
filterlim (fun z => mult (fst z) (snd z)) (filter_prod (locally x) (locally y)) (locally (mult x y)).
Lemma filterlim_locally_ball_norm :
forall {K : AbsRing} {T} {U : NormedModule K} {F : (T -> Prop) -> Prop} {FF : Filter F} (f : T -> U) (y : U),
filterlim f F (locally y) <-> forall eps : posreal, F (fun x => ball_norm y eps (f x)).