Varieties of abelian topological groups and scattered spaces

The variety of topological groups generated by the class of all abelian k_omega-groups has been shown to equal the variety of topological groups generated by the free abelian topological group on [0,1]. In this paper it is proved that the free abelian topological group on a compact Hausdorff space, X, generates the same variety if and only if X is not scattered.