Year: 2017
Type: article
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.
Author: Takayuki Kihara
Institution: University of California, Berkeley
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W2482249279