Lipschitz properties of semi-analytic sets

Adam Parusiński

Annales de l'institut Fourier (1988)

  • Volume: 38, Issue: 4, page 189-213
  • ISSN: 0373-0956

Abstract

top
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.

How to cite

top

Parusiński, Adam. "Lipschitz properties of semi-analytic sets." Annales de l'institut Fourier 38.4 (1988): 189-213. <http://eudml.org/doc/74815>.

@article{Parusiński1988,
abstract = {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.},
author = {Parusiński, Adam},
journal = {Annales de l'institut Fourier},
keywords = {Lipschitz stratification; semi-analytic sets; L-stratification; regular projections; L-regular sets; Lipschitz vector fields},
language = {eng},
number = {4},
pages = {189-213},
publisher = {Association des Annales de l'Institut Fourier},
title = {Lipschitz properties of semi-analytic sets},
url = {http://eudml.org/doc/74815},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Parusiński, Adam
TI - Lipschitz properties of semi-analytic sets
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 4
SP - 189
EP - 213
AB - 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.
LA - eng
KW - Lipschitz stratification; semi-analytic sets; L-stratification; regular projections; L-regular sets; Lipschitz vector fields
UR - http://eudml.org/doc/74815
ER -

References

top
  1. [1] S. BANACH, Wstep do teorii funkcji rzeczywistych, Monografie Matematyczne, Warszawa-Wroclaw, 1951. 
  2. [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. Zbl0435.32006MR81i:32003
  3. [3] H. HIRONAKA, Introduction to real-analytic sets and real-analytic maps, Inst. Mat. "L. Tonelli", Pisa, 1973. 
  4. [4] S. LOJASIEWICZ, Ensembles semi-analytiques, Inst. Hautes Sci. Publ. Math., Paris, 1965. Zbl0241.32005
  5. [5] J. MATHER, Stratifications and mappings, Proc. Dynamical Systems Conference, Salvador, Brazil, 1971, Acad. Press. 
  6. [6] T. MOSTOWSKI, Lipschitz equisingularity, Dissertationes Math., 243 (1985). Zbl0578.32020MR87e:32008
  7. [7] A. PARUSIŃSKI, Lipschitz stratification of real analytic sets, to appear in "Singularities", Banach Center Publ., Vol. 20. Zbl0666.32011MR92a:32009
  8. [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. Zbl0574.32010MR86j:32015
  9. [9] J. L. VERDIER, Stratification de Whitney et théorème de Bertini-Sard, Invent. Math., 36 (1976), 295-312. Zbl0333.32010MR58 #1242

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.