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  1. Continuous reducibility and dimension of metric spaces.Philipp Schlicht - 2018 - Archive for Mathematical Logic 57 (3-4):329-359.
    If is a Polish metric space of dimension 0, then by Wadge’s lemma, no more than two Borel subsets of X are incomparable with respect to continuous reducibility. In contrast, our main result shows that for any metric space of positive dimension, there are uncountably many Borel subsets of that are pairwise incomparable with respect to continuous reducibility. In general, the reducibility that is given by the collection of continuous functions on a topological space \\) is called the Wadge quasi-order (...)
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  • Game representations of classes of piecewise definable functions.Luca Motto Ros - 2011 - Mathematical Logic Quarterly 57 (1):95-112.
    We present a general way of defining various reduction games on ω which “represent” corresponding topologically defined classes of functions. In particular, we will show how to construct games for piecewise defined functions, for functions which are pointwise limit of certain sequences of functions and for Γ-measurable functions. These games turn out to be useful as a combinatorial tool for the study of general reducibilities for subsets of the Baire space [10].
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