A Q-Wadge Hierarchy in Quasi-Polish Spaces [article]

Victor Selivanov
2019 arXiv   pre-print
The Wadge hierarchy was originally defined and studied only in the Baire space (and some other zero-dimensional spaces). We extend it here to arbitrary topological spaces by providing a set-theoretic definition of all its levels. We show that our extension behaves well in second countable spaces and especially in quasi-Polish spaces. In particular, all levels are preserved by continuous open surjections between second countable spaces which implies e.g. several Hausdorff-Kuratowski-type
more » ... in quasi-Polish spaces. In fact, many results hold not only for the Wadge hierarchy of sets but also for its extension to Borel functions from a space to a countable better quasiorder Q.
arXiv:1911.02758v1 fatcat:upw6m74aebajjitaamdtsmu6ky