A dichotomy characterizing analytic digraphs of uncountable Borel chromatic number in any dimension
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- by Dominique Lecomte PDF
- Trans. Amer. Math. Soc. 361 (2009), 4181-4193 Request permission
Abstract:
We study the extension of the Kechris-Solecki-Todorčević dichoto-my 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
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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
- MR Author ID: 336400
- Email: dominique.lecomte@upmc.fr
- 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.
- © Copyright 2009 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 361 (2009), 4181-4193
- MSC (2000): Primary 03E15; Secondary 54H05
- DOI: https://doi.org/10.1090/S0002-9947-09-04792-8
- MathSciNet review: 2500884