Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension


Author: Dominique Lecomte
Journal: Trans. Amer. Math. Soc. 361 (2009), 4181-4193
MSC (2000): Primary 03E15; Secondary 54H05
Published electronically: February 10, 2009
MathSciNet review: 2500884
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the extension of the Kechris-Solecki-Todorčević dichotomy on analytic graphs to dimensions higher than 2. We prove that the extension is possible in any dimension, finite or infinite. The original proof works in the case of the finite dimension. We first prove that the natural extension does not work in the case of the infinite dimension, for the notion of continuous homomorphism used in the original theorem. Then we solve the problem in the case of the infinite dimension. Finally, we prove that the natural extension works in the case of the infinite dimension, but for the notion of Baire-measurable homomorphism.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 03E15, 54H05

Retrieve articles in all journals with MSC (2000): 03E15, 54H05


Additional Information

Dominique Lecomte
Affiliation: Equipe d’Analyse Fonctionnelle, Université Paris 6, tour 46-0, boîte 186, 4, place Jussieu, 75 252 Paris Cedex 05, France
Address at time of publication: Université de Picardie, I.U.T. de l’Oise, site de Creil,13, allée de la faïencerie, 60 107 Creil, France
Email: dominique.lecomte@upmc.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04792-8
PII: S 0002-9947(09)04792-8
Keywords: Borel chromatic number, dimension
Received by editor(s): July 23, 2007
Published electronically: February 10, 2009
Additional Notes: The author would like to thank the anonymous referee for the simplification of some proofs in this paper.
Article copyright: © Copyright 2009 American Mathematical Society