Section Open.
Context {T : UniformSpace}.
Definition open (D : T -> Prop) :=
forall x, D x -> locally x D.
End Open.

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