Tests \`a la Hurewicz dans le plan

TL;DR

This paper characterizes certain Borel sets in product spaces that cannot be simplified into transfinite differences of open sets through topology changes, extending Hurewicz-like criteria.

Contribution

It provides a new Hurewicz-like characterization for Borel sets with countable sections in product Polish spaces, including those resistant to topological simplification.

Findings

Identifies Borel sets that resist topological simplification.

Extends Hurewicz-like criteria to product spaces.

Includes sets with countable sections.

Abstract

We give, for some Borel sets of a product of two Polish spaces, including the Borel sets with countable sections, a Hurewicz-like characterization of those which cannot become a transfinite difference of open sets by changing the two Polish topologies.