  We define and study an effective version of the Wadge hierarchy in computable
quasi-Polish spaces which include most spaces of interest for computable
analysis. Along with hierarchies of sets we study hierarchies of k-partitions
which are interesting on their own. We show that levels of such hierarchies are
preserved by the computable effectively open surjections, that if the effective
Hausdorff-Kuratowski theorem holds in the Baire space then it holds in every
computable quasi-Polish space, and we extend the effective Hausdorff theorem to
k-partitions.
