We establish some results on some variants of the Hausdorff difference hierarchy. In particular, we extend the recently developed theory of difference hierarchy over the open sets in ω-algebraic domains to a similar theory for ω-continuous domains, and prove some analogs of the Hausdorff-Kuratowski theorem for kpartitions. We discuss also a broad class of effective topological spaces closely relevant to our study of the difference hierarchy and to computability in topology.