K-subanalytic rectilinearization and uniformization

Artur Piękosz

Open Mathematics (2003)

  • Volume: 1, Issue: 4, page 441-456
  • ISSN: 2391-5455

Abstract

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We prove rectilinearization and uniformization theorems for K-subanalytic (∝anK-definable) sets and functions using the Lion-Rolin formula. Parallel reasoning gives standard results for the subanalytic case.

How to cite

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Artur Piękosz. "K-subanalytic rectilinearization and uniformization." Open Mathematics 1.4 (2003): 441-456. <http://eudml.org/doc/268800>.

@article{ArturPiękosz2003,
abstract = {We prove rectilinearization and uniformization theorems for K-subanalytic (∝anK-definable) sets and functions using the Lion-Rolin formula. Parallel reasoning gives standard results for the subanalytic case.},
author = {Artur Piękosz},
journal = {Open Mathematics},
keywords = {32B20; 14P15},
language = {eng},
number = {4},
pages = {441-456},
title = {K-subanalytic rectilinearization and uniformization},
url = {http://eudml.org/doc/268800},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Artur Piękosz
TI - K-subanalytic rectilinearization and uniformization
JO - Open Mathematics
PY - 2003
VL - 1
IS - 4
SP - 441
EP - 456
AB - We prove rectilinearization and uniformization theorems for K-subanalytic (∝anK-definable) sets and functions using the Lion-Rolin formula. Parallel reasoning gives standard results for the subanalytic case.
LA - eng
KW - 32B20; 14P15
UR - http://eudml.org/doc/268800
ER -

References

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  3. [3] L. van den Dries and C. Miller: “Extending Tamm's theorem”, Ann. Inst. Fourier, Grenoble, Vol. 44, (1994), pp. 1367–1395. Zbl0816.32004
  4. [4] L. van den Dries and C. Miller: “Geometric categories and o-minimal structures”, Duke Math. Journal, Vol. 84, (1996), pp. 497–540. http://dx.doi.org/10.1215/S0012-7094-96-08416-1 Zbl0889.03025
  5. [5] H. Hironaka: Introduction to real-analytic sets and real-analytic maps, Inst. Matem. “L. Tonelli”, Pisa, 1973. 
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  7. [7] C. Miller: “Expansions of the real field with power functions”, Ann. Pure Appl. Logic, Vol. 68, (1994), pp. 79–84. http://dx.doi.org/10.1016/0168-0072(94)90048-5 
  8. [8] A. Parusiński: “Subanalytic functions”, Trans. Amer. Math. Soc., Vol. 344, (1994), pp. 583–595. http://dx.doi.org/10.2307/2154496 Zbl0819.32006
  9. [9] A. Parusiński: “Lipschitz stratification of subanalytic sets”, Ann. Scient. Éc. Norm. Sup., 4e série, t. 27, (1994), pp. 661–696. Zbl0819.32007
  10. [10] A. Parusiński: “On the preparation theorem for subanalytic functions”, In: D. Siersma, C.T.C. Wall, V. Zakalyukin, (Eds.): New developments in singularity theory (Cambridge 2000), Kluwer Acad. Publ., 2001, pp. 193–215. Zbl0994.32007
  11. [11] J.-Cl. Tougeron: “Paramétrisations de petits chemins en géométrie analytique réelle”, In: Singularities and differential equations (Warsaw 1993), Banach Center Publications, Vol. 33, (1996), pp. 421–436. 

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