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ArticleOriginal scientific text

Title

A counterexample to subanalyticity of an arc-analytic function

Authors 1

Affiliations

  1. Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Abstract

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

Bibliography

  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.
  4. [K1] K. Kurdyka, Points réguliers d'un sous-analytique, Ann. Inst. Fourier (Grenoble) 38 (1) (1988), 133-156.
  5. [K2] K. Kurdyka, Ensembles semi-algébriques symétriques par arcs, Math. Ann. 282 (1988), 445-462.
Annales Polonici Mathematici
1991/55/1
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Pages:
241-243
Main language of publication
English
Received
1990-08-16
Published
1991
Exact and natural sciences