Classes de Wadge potentielles et theor`emes duniformisation partielle

We want to give a construction as simple as possible of a Borel subset of a product of two Polish spaces. This introduces the notion of potential Wadge class. Among other things, we study the non-potentially closed sets, by proving Hurewicz-like results. This leads to partial uniformization theorems, on big sets, in the sense of cardinality or Baire category.

💡 Research Summary

The paper introduces the notion of a “potential Wadge class” as a natural extension of the classical Wadge hierarchy, which traditionally orders subsets of Polish spaces according to continuous reducibility. In the new framework, a Borel set A⊆X×Y is said to belong to a potential Wadge class C if there exist continuous maps f:X→X′ and g:Y→Y′ such that the image (f×g)