(** ** Closed sets in uniform spaces *)
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_ext :
forall D E : T -> Prop,
(forall x, D x <-> E x) ->
closed D -> closed E.