Section Closed.
Context {T : UniformSpace}.
Definition closed (D : T -> Prop) :=
forall x, not (locally x (fun x : T => not (D x))) -> D x.
(* Lemma closed_or : forall D E : T -> Prop, closed D -> closed E -> closed (fun x => D x \/ E x). *)
End Closed.

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)).