Definition AbsRing_UniformSpace_mixin :=
UniformSpace.Mixin _ _ AbsRing_ball_center AbsRing_ball_sym AbsRing_ball_triangle.
Canonical AbsRing_UniformSpace :=
UniformSpace.Pack K AbsRing_UniformSpace_mixin K.
End AbsRing_UniformSpace.
(** Functional metric spaces *)
Section fct_UniformSpace.
Variable (T : Type) (U : UniformSpace).
Definition fct_ball (x : T -> U) (eps : R) (y : T -> U) :=
forall t : T, ball (x t) eps (y t).

(* Specifications: *)
Lemma fct_ball_center :
forall (x : T -> U) (e : posreal),
fct_ball x e x.
Lemma fct_ball_sym :
forall (x y : T -> U) (e : R),
fct_ball x e y -> fct_ball y e x.
Lemma fct_ball_triangle :
forall (x y z : T -> U) (e1 e2 : R),
fct_ball x e1 y -> fct_ball y e2 z -> fct_ball x (e1 + e2) z.