[Distinguished trees, double-trees and lifting theorems]
We introduce the notion of distinguished tree relation and give applications. We prove in ZFC an old conjecture of A.V. Ostrovsky about the image of a Borel space under a compact covering mapping. We also prove that if is countable then any compact covering mapping from a Δ11 space onto a Σ01+ξ+2 or Π01+ξ+2 space is inductively perfect. The converse of last statement is shown.
On introduit la notion de relation d'arbre distinguée dans une autre et on en donne des applications. On démontre dans ZFC une ancienne conjecture d'A.V. Ostrovsky sur l'image semi-propre d'un borélien. On montre aussi que si est dénombrable toute application semi-propre d'un espace Δ11 sur un espace Σ01+ξ+2 ou Π01+ξ+2 est inductivement propre. La réciproque de ce dernier énoncé est établie.
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Gabriel Debs 1; Jean Saint Raymond 1
@article{CRMATH_2003__336_8_625_0, author = {Gabriel Debs and Jean Saint Raymond}, title = {Arbres distingu\'es, bi-arbres et th\'eor\`emes de rel\`evement}, journal = {Comptes Rendus. Math\'ematique}, pages = {625--628}, publisher = {Elsevier}, volume = {336}, number = {8}, year = {2003}, doi = {10.1016/S1631-073X(03)00150-X}, language = {fr}, }
Gabriel Debs; Jean Saint Raymond. Arbres distingués, bi-arbres et théorèmes de relèvement. Comptes Rendus. Mathématique, Volume 336 (2003) no. 8, pp. 625-628. doi : 10.1016/S1631-073X(03)00150-X. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00150-X/
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