Borel-piecewise continuous reducibility for uniformization problems

We study a fine hierarchy of Borel-piecewise continuous functions, especially, between closed-piecewise continuity and $G_\delta$-piecewise continuity. Our aim is to understand how a priority argument in computability theory is connected to the notion of $G_\delta$-piecewise continuity, and then we utilize this connection to obtain separation results on subclasses of $G_\delta$-piecewise continuous reductions for uniformization problems on set-valued functions with compact graphs. This method is also applicable for separating various non-constructive principles in the Weihrauch lattice.

我们研究了波莱尔分段连续函数的一个精细层次结构，特别是在闭分段连续性和\(G_\delta\) - 分段连续性之间。我们的目的是理解可计算性理论中的优先论证如何与\(G_\delta\) - 分段连续性的概念相关联，然后我们利用这种关联来获得具有紧图像的集值函数的一致化问题的\(G_\delta\) - 分段连续归约子类的分离结果。这种方法也适用于分离魏赫拉赫格中的各种非构造性原理。