Séminaires : Séminaire Général de Logique

Equipe(s) : lm,
Responsables :S. Anscombe, A. Khélif, A. Vignati
Email des responsables : sylvy.anscombe@imj-prg.fr, vignati@imj-prg.fr
Salle : 1013
Adresse :Sophie Germain

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Orateur(s) Christian Rosendal - University of Illinois at Chicago,
Titre Continuity of universally measurable homomorphisms
Horaire16:00 à 17:15

We show that a universally measurable homomorphism between Polish
groups is automatically continuous. Using our general analysis of
continuity of group homomorphisms, this result is used to calibrate the
strength of the existence of a discontinuous homomorphism between Polish
groups. In particular, it is shown that, modulo ZF+DC, the existence of
a discontinuous homomorphism between Polish groups implies that the
Hamming graph on {0, 1}N has finite chromatic number. This solves a
classical problem originating in JPR Christensen's work on Haar null sets.

AdresseSophie Germain