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). *)

Lemma closed_false :
closed (fun x : T => False).