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.

@article{Kihara16,
  title = {Borel-Piecewise Continuous Reducibility for Uniformization Problems},
  author = {Takayuki Kihara},
  journal = {Logical Methods in Computer Science},
  volume = {12},
  number = {4},
  year = {2017},
  doi = {10.2168/lmcs-12(4:4)2016}
}