Baire class one colorings and a dichotomy for countable unions of $F_\sigma$ rectangles

Dominique Lecomte (1)

1 IMJ - Institut de Mathématiques de Jussieu

We study the Baire class one countable colorings, i.e., the countable partitions into $F_\sigma$ sets. Such a partition gives a covering of the diagonal into countably many $F_\sigma$ squares. This leads to the study of countable unions of $F_\sigma$ rectangles. We give a Hurewicz-like dichotomy for such countable unions.

Mots clés: Baire class one; Borel chromatic number; Borel class; coloring; dichotomy; Hurewicz; partition; product

Domaines: Logique [math.LO]; Topologie générale [math.GN]

Dominique Lecomte. Baire class one colorings and a dichotomy for countable unions of $F_\sigma$ rectangles. 2010. ⟨hal-00472830⟩