Borel-piecewise continuous reducibility for uniformization problems

Abstract

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.

References in corpus (3)

• On the algebraic structure of Weihrauch degrees
• Game characterizations and lower cones in the Weihrauch degrees
• A topological view on algebraic computation models