Section Locally.
Context {T : UniformSpace}.
Definition locally (x : T) (P : T -> Prop) :=
exists eps : posreal, forall y, ball x eps y -> P y.
Global Instance locally_filter :
forall x : T, ProperFilter (locally x).

Lemma locally_locally :
forall (x : T) (P : T -> Prop),
locally x P -> locally x (fun y => locally y P).