An arc-analytic function with nondiscrete singular set

• Autorzy: Krzysztof Kurdyka
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

arc-analytic; blow-up; projective limit; strict transform

Kategorie tematyczne

• 32B20: Semi-analytic sets and subanalytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994
• Tom: 59
• Numer: 3
• Strony: 251-254

Daty

wydano

1994

otrzymano

1993-05-27

Twórcy

autor

Krzysztof Kurdyka

• Laboratorie de Mathématiques, Université de Savoie, Campus Scientifique, 73376 Le Bourget-du-Lac Cedex, France

Bibliografia

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• [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.
• [G] H. Grauert, On Levi's problem and the imbedding of real-analytic manifolds, Ann. of Math. 68 (1958), 460-472.
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• [K2] K. Kurdyka, Ensembles semi-algébriques symétriques par arcs, Math. Ann. 282 (1988), 445-462.
• [K3] K. Kurdyka, A counterexample to subanalyticity of an arc-analytic function, Ann. Polon. Math. 55 (1991), 241-243.
• [P] A. Parusiński, Subanalytic functions, Trans. Amer. Math. Soc., to appear.
• [T] M. Tamm, Subanalytic sets in the calculus of variations, Acta Math. 146 (1981), 167-199.