Complexit\'e des bor\'eliens \`a coupes d\'enombrables

TL;DR

This paper characterizes Borel subsets with countable sections in product Polish spaces, identifying their complexity levels and topological properties related to their classification within the Borel hierarchy.

Contribution

It provides a Hurewicz-like characterization for each complexity level L of certain Borel subsets, linking their topological and descriptive set-theoretic properties.

Findings

Characterization of Borel subsets with countable sections at each complexity level L.

Identification of conditions preventing subsets from becoming simpler through topology changes.

Extension of Hurewicz-like theorems to complex Borel structures.

Abstract

We give, for each level of complexity L, a Hurewicz-like characterization of the Borel subsets with countable sections of a product of two Polish spaces that cannot become in L by changing the two Polish topologies.