Some observations on "A new proof of a theorem of Jayne and Rogers"

TL;DR

This paper corrects a mistake in a previous proof of the Jayne-Rogers theorem, extends it to regular topological spaces, and generalizes Solecki's sharpening to non-separable spaces.

Contribution

It provides a corrected proof of the Jayne-Rogers theorem and extends key results to broader classes of topological spaces.

Findings

Corrected proof of the Jayne-Rogers theorem

Extension of the theorem to regular topological spaces

Generalization of Solecki's sharpening to non-separable spaces

Abstract

We adapt a construction taken from `L. Motto Ros and B. Semmes, A new proof of a theorem of Jayne and Rogers, Real Anal. Exchange 35(1) (2009/2010), 195-204' in order to correct a mistake contained in the first part of the same paper. As a byproduct of the new construction, the Jayne-Rogers theorem is extended to functions whose range is a regular topological space, and a theorem of Solecki which sharpens the Jayne-Rogers theorem for separable metric spaces is extended to the non-separable context.