A counterexample to subanalyticity of an arc-analytic function

Krzysztof Kurdyka

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 241-243
  • ISSN: 0066-2216

Abstract

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We construct an arc-analytic function (i.e. a function analytic on each analytic arc) whose graph is not subanalytic.

How to cite

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Krzysztof Kurdyka. "A counterexample to subanalyticity of an arc-analytic function." Annales Polonici Mathematici 55.1 (1991): 241-243. <http://eudml.org/doc/262340>.

@article{KrzysztofKurdyka1991,
abstract = {We construct an arc-analytic function (i.e. a function analytic on each analytic arc) whose graph is not subanalytic.},
author = {Krzysztof Kurdyka},
journal = {Annales Polonici Mathematici},
keywords = {subanalyticity; arc-analytic function},
language = {eng},
number = {1},
pages = {241-243},
title = {A counterexample to subanalyticity of an arc-analytic function},
url = {http://eudml.org/doc/262340},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Krzysztof Kurdyka
TI - A counterexample to subanalyticity of an arc-analytic function
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 241
EP - 243
AB - We construct an arc-analytic function (i.e. a function analytic on each analytic arc) whose graph is not subanalytic.
LA - eng
KW - subanalyticity; arc-analytic function
UR - http://eudml.org/doc/262340
ER -

References

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  1. [BM] E. Bierstone and P. D. Milman, Arc-analytic functions, preprint, Univ. of Toronto, 1989. 
  2. [D] G. Dloussky, Analycité séparée et prolongement analytique, preprint, Univ. de Marseille, 1989. 
  3. [G] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472. Zbl0108.07804
  4. [K1] K. Kurdyka, Points réguliers d'un sous-analytique, Ann. Inst. Fourier (Grenoble) 38 (1) (1988), 133-156. Zbl0619.32007
  5. [K2] K. Kurdyka, Ensembles semi-algébriques symétriques par arcs, Math. Ann. 282 (1988), 445-462. Zbl0686.14027

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