Definition closed (D : T -> Prop) :=
  forall x, not (locally x (fun x : T => not (D x))) -> D x.

Lemma closed_comp : forall {T U : UniformSpace} (f : T -> U) (D : U -> Prop), (forall x, filterlim f (locally x) (locally (f x))) -> closed D -> closed (fun x : T => D (f x)).