Lipschitz stratifications in o-minimal structures
[Stratifications lipschitziennes dans les structures o-minimales]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 2, pp. 399-421.

Cet article établit l'existence des stratifications lipschitziennes au sens de Mostowski pour les ensembles définissables dans une structure o-minimale polynomialement bornée. On améliore aussi le théorème de préparation de L. van den Dries et P. Speissegger.

This paper establishes existence of Lipschitz stratifications in the sense of Mostowski for sets which are definable in a polynomially bounded o-minimal structure. We also improve L. van den Dries and P. Speissegger's preparation theorem for definable functions.

Publié le :
DOI : 10.24033/asens.2286
Classification : 57N80, 03C64; 32S15, 14P10
Keywords: O-minimal-structures, definable sets, polynomially bounded, Lipschitz geometry, stratifications, regularity conditions, equisingularity.
Mot clés : Structures o-minimales, ensembles définissables, polynomialement borné, géométrie lipschitzienne, stratifications, conditions de régularité, équisingularité. 
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     title = {Lipschitz stratifications  in o-minimal structures},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {399--421},
     publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
     volume = {Ser. 4, 49},
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Nguyen, Nhan; Valette, Guillaume. Lipschitz stratifications  in o-minimal structures. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 49 (2016) no. 2, pp. 399-421. doi : 10.24033/asens.2286. http://www.numdam.org/articles/10.24033/asens.2286/

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