no. 4
Lipschitz properties of semi-analytic sets
Annales de l'Institut Fourier, Tome 38 (1988) no. 4, pp. 189-213.

L’existence de stratification lipschitzienne, au sens de Mostowski, pour les ensembles semi-analytiques compacts est prouvée; (cette stratification donne la constance du type lipschitzienne le long de chaque strate). La preuve ne dépend pas du cas complexe, considéré par Mostowski, et donne aussi quelques autres propriétés lipschitziennes des ensembles semi-analytiques.

The existence of Lipschitz stratification, in the sense of Mostowski, for compact semi-analytic sets is proved. (This stratification ensures the constance of the Lipschitz type along each stratum). The proof is independent of the complex case, considered by Mostowski, and gives also some other Lipschitz properties of semi-analytic sets.

@article{AIF_1988__38_4_189_0,
     author = {Parusi\'nski, Adam},
     title = {Lipschitz properties of semi-analytic sets},
     journal = {Annales de l'Institut Fourier},
     pages = {189--213},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {38},
     number = {4},
     year = {1988},
     doi = {10.5802/aif.1154},
     zbl = {0631.32006},
     mrnumber = {90e:32016},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1154/}
}
TY  - JOUR
AU  - Parusiński, Adam
TI  - Lipschitz properties of semi-analytic sets
JO  - Annales de l'Institut Fourier
PY  - 1988
SP  - 189
EP  - 213
VL  - 38
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1154/
DO  - 10.5802/aif.1154
LA  - en
ID  - AIF_1988__38_4_189_0
ER  - 
%0 Journal Article
%A Parusiński, Adam
%T Lipschitz properties of semi-analytic sets
%J Annales de l'Institut Fourier
%D 1988
%P 189-213
%V 38
%N 4
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1154/
%R 10.5802/aif.1154
%G en
%F AIF_1988__38_4_189_0
Parusiński, Adam. Lipschitz properties of semi-analytic sets. Annales de l'Institut Fourier, Tome 38 (1988) no. 4, pp. 189-213. doi : 10.5802/aif.1154. https://aif.centre-mersenne.org/articles/10.5802/aif.1154/

[1] S. Banach, Wstep do teorii funkcji rzeczywistych, Monografie Matematyczne, Warszawa-Wroclaw, 1951.

[2] Z. Denkowska, S. Lojasiewicz, J. Stasica, Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Pol. Acad. Sci. (Math), Vol. 27, N° 7-8 (1979), 530-536. | MR | Zbl

[3] H. Hironaka, Introduction to real-analytic sets and real-analytic maps, Inst. Mat. "L. Tonelli", Pisa, 1973.

[4] S. Lojasiewicz, Ensembles semi-analytiques, Inst. Hautes Sci. Publ. Math., Paris, 1965.

[5] J. Mather, Stratifications and mappings, Proc. Dynamical Systems Conference, Salvador, Brazil, 1971, Acad. Press.

[6] T. Mostowski, Lipschitz equisingularity, Dissertationes Math., 243 (1985). | MR | Zbl

[7] A. Parusiński, Lipschitz stratification of real analytic sets, to appear in "Singularities", Banach Center Publ., Vol. 20. | MR | Zbl

[8] W. Pawlucki, Le théorème de Puiseux pour une application sous-analytique, Bull. Pol. Acad. Sci. (Math), Vol. 32, N° 9-10 (1984), 555-560. | MR | Zbl

[9] J. L. Verdier, Stratification de Whitney et théorème de Bertini-Sard, Invent. Math., 36 (1976), 295-312. | MR | Zbl

Cité par Sources :