On minimal non-potentially closed subsets of the plane |
| |
Authors: | Dominique Lecomte |
| |
Affiliation: | a Université Paris 6, Equipe d'Analyse Fonctionnelle, Tour 46-0, boîte 186, 4 place Jussieu, 75252 Paris cedex 05, France b Université de Picardie, IUT de l'Oise, site de Creil, 13, allée de la faïencerie, 60107 Creil, France |
| |
Abstract: | We study the Borel subsets of the plane that can be made closed by refining the Polish topology on the real line. These sets are called potentially closed. We first compare Borel subsets of the plane using products of continuous functions. We show the existence of a perfect antichain made of minimal sets among non-potentially closed sets. We apply this result to graphs, quasi-orders and partial orders. We also give a non-potentially closed set minimum for another notion of comparison. Finally, we show that we cannot have injectivity in the Kechris-Solecki-Todor?evi? dichotomy about analytic graphs. |
| |
Keywords: | primary, 03E15 secondary, 54H05 |
本文献已被 ScienceDirect 等数据库收录! |
|