An arc-analytic function with nondiscrete singular set

Krzysztof Kurdyka

Annales Polonici Mathematici (1994)

  • Volume: 59, Issue: 3, page 251-254
  • ISSN: 0066-2216

Abstract

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We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².

How to cite

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Krzysztof Kurdyka. "An arc-analytic function with nondiscrete singular set." Annales Polonici Mathematici 59.3 (1994): 251-254. <http://eudml.org/doc/262357>.

@article{KrzysztofKurdyka1994,
abstract = {We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².},
author = {Krzysztof Kurdyka},
journal = {Annales Polonici Mathematici},
keywords = {arc-analytic; blow-up; projective limit; strict transform; subanalytic sets; arc-analytic functions},
language = {eng},
number = {3},
pages = {251-254},
title = {An arc-analytic function with nondiscrete singular set},
url = {http://eudml.org/doc/262357},
volume = {59},
year = {1994},
}

TY - JOUR
AU - Krzysztof Kurdyka
TI - An arc-analytic function with nondiscrete singular set
JO - Annales Polonici Mathematici
PY - 1994
VL - 59
IS - 3
SP - 251
EP - 254
AB - We construct an arc-analytic function (i.e. analytic on every real-analytic arc) in ℝ² which is analytic outside a nondiscrete subset of ℝ².
LA - eng
KW - arc-analytic; blow-up; projective limit; strict transform; subanalytic sets; arc-analytic functions
UR - http://eudml.org/doc/262357
ER -

References

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  1. [BM] E. Bierstone and P. D. Milman, Arc-analytic functions, Invent. Math. 101 (1990), 411-424. Zbl0723.32005
  2. [BMP] E. Bierstone, P. D. Milman and A. Parusiński, A function which is arc-analytic but not continuous, Proc. Amer. Math. Soc. 113 (1991), 419-423. Zbl0739.32009
  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
  6. [K3] K. Kurdyka, A counterexample to subanalyticity of an arc-analytic function, Ann. Polon. Math. 55 (1991), 241-243. Zbl0752.32005
  7. [P] A. Parusiński, Subanalytic functions, Trans. Amer. Math. Soc., to appear. Zbl0819.32006
  8. [T] M. Tamm, Subanalytic sets in the calculus of variations, Acta Math. 146 (1981), 167-199. Zbl0478.58010

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