# An arc-analytic function with nondiscrete singular set

Annales Polonici Mathematici (1994)

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

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topKrzysztof 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

top- [BM] E. Bierstone and P. D. Milman, Arc-analytic functions, Invent. Math. 101 (1990), 411-424. Zbl0723.32005
- [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
- [G] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472. Zbl0108.07804
- [K1] K. Kurdyka, Points réguliers d'un sous-analytique, Ann. Inst. Fourier (Grenoble) 38 (1) (1988), 133-156. Zbl0619.32007
- [K2] K. Kurdyka, Ensembles semi-algébriques symétriques par arcs, Math. Ann. 282 (1988), 445-462. Zbl0686.14027
- [K3] K. Kurdyka, A counterexample to subanalyticity of an arc-analytic function, Ann. Polon. Math. 55 (1991), 241-243. Zbl0752.32005
- [P] A. Parusiński, Subanalytic functions, Trans. Amer. Math. Soc., to appear. Zbl0819.32006
- [T] M. Tamm, Subanalytic sets in the calculus of variations, Acta Math. 146 (1981), 167-199. Zbl0478.58010

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