Definition extension_approximation: point_set X -> point_set RTop.

(* Specifications: *)
Lemma extension_approximation_bound: forall x:point_set X, -1/3 <= extension_approximation x <= 1/3.
Lemma extension_approximation_diff_bound: forall x:point_set (SubspaceTopology F), -2/3 <= f0 x - extension_approximation (subspace_inc F x) <= 2/3.
Lemma extension_approximation_continuous: continuous extension_approximation.
Lemma missing_pow_mult: forall (x y:R) (n:nat), (x*y)^n = x^n * y^n.