On the Difference Hierarchy in Countably Based T0-Spaces

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 @w-algebraic domains to a similar theory for @w-continuous domains, and prove some analogs of the Hausdorff-Kuratowski theorem for k-partitions. We discuss also a broad class of effective topological spaces closely relevant to our study of the difference hierarchy and to computability in topology.

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