# Wadge-like reducibilities on arbitrary quasi-Polish spaces

@article{Ros2014WadgelikeRO,
title={Wadge-like reducibilities on arbitrary quasi-Polish spaces},
author={Luca Motto Ros and Philipp Schlicht and Victor L. Selivanov},
journal={Mathematical Structures in Computer Science},
year={2014},
volume={25},
pages={1705 - 1754}
}
• Published 24 April 2012
• Mathematics
• Mathematical Structures in Computer Science
The structure of the Wadge degrees on zero-dimensional spaces is very simple (almost well ordered), but for many other natural nonzero-dimensional spaces (including the space of reals) this structure is much more complicated. We consider weaker notions of reducibility, including the so-called Δ0 α-reductions, and try to find for various natural topological spaces X the least ordinal α X such that for every α X ⩽ β < ω1 the degree-structure induced on X by the Δ0 β-reductions is simple (i.e…
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