Let X = S ⊕ G, where S is a countable abelian semigroup and G is a countably infinite abelian group such that {2g : g ∈ G} is infinite. Let π : X → G be the projection map defined by π(s, g) = g for all x = (s, g) ∈ X. Let f : X → N0 ∪ {∞} be any map such that the set π ( f(0) ) is a finite subset of G. Then there exists a set B ⊆ X such that r̂B(x) = f(x… (More)