Subanalytic functions
HTML articles powered by AMS MathViewer
- by Adam Parusiński
- Trans. Amer. Math. Soc. 344 (1994), 583-595
- DOI: https://doi.org/10.1090/S0002-9947-1994-1160156-4
- PDF | Request permission
Abstract:
We prove a strong version of rectilinearization theorem for subanalytic functions. Then we use this theorem to study the properties of arc-analytic functions.References
- Daniel Barlet, Majoration du volume des fibres génériques et forme géométrique du théorème d’aplatissement, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 1, A29–A31 (French, with English summary). MR 522012
- Edward Bierstone and Pierre D. Milman, Semianalytic and subanalytic sets, Inst. Hautes Études Sci. Publ. Math. 67 (1988), 5–42. MR 972342
- Edward Bierstone and Pierre D. Milman, Arc-analytic functions, Invent. Math. 101 (1990), no. 2, 411–424. MR 1062969, DOI 10.1007/BF01231509
- E. Bierstone, P. D. Milman, and A. Parusiński, A function which is arc-analytic but not continuous, Proc. Amer. Math. Soc. 113 (1991), no. 2, 419–423. MR 1072083, DOI 10.1090/S0002-9939-1991-1072083-4
- J. Denef and L. van den Dries, $p$-adic and real subanalytic sets, Ann. of Math. (2) 128 (1988), no. 1, 79–138. MR 951508, DOI 10.2307/1971463
- Zofia Denkowska, Stanisław Łojasiewicz, and Jacek Stasica, Certaines propriétés élémentaires des ensembles sous-analytiques, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), no. 7-8, 529–536 (1980) (French, with English and Russian summaries). MR 581546
- Heisuke Hironaka, Introduction to real-analytic sets and real-analytic maps, Quaderni dei Gruppi di Ricerca Matematica del Consiglio Nazionale delle Ricerche, Università di Pisa, Istituto Matematico “L. Tonelli”, Pisa, 1973. MR 0477121
- Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; 79 (1964), 205–326. MR 0199184, DOI 10.2307/1970547
- Heisuke Hironaka, Stratification and flatness, Real and complex singularities (Proc. Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976) Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, pp. 199–265. MR 0499286
- Heisuke Hironaka, Monique Lejeune-Jalabert, and Bernard Teissier, Platificateur local en géométrie analytique et aplatissement local, Singularités à Cargèse (Rencontre Singularités Géom. Anal., Inst. Études Sci., Cargèse, 1972) Astérisque, Nos. 7 et 8, Soc. Math. France, Paris, 1973, pp. 441–463. MR 0409884
- Krzysztof Kurdyka, Points réguliers d’un sous-analytique, Ann. Inst. Fourier (Grenoble) 38 (1988), no. 1, 133–156 (French, with English summary). MR 949002
- Krzysztof Kurdyka, Ensembles semi-algébriques symétriques par arcs, Math. Ann. 282 (1988), no. 3, 445–462 (French). MR 967023, DOI 10.1007/BF01460044
- Tzee Char Kuo, On classification of real singularities, Invent. Math. 82 (1985), no. 2, 257–262. MR 809714, DOI 10.1007/BF01388802 A. Parusiński, Lipschitz stratification of subanalytic sets, Ann. École Norm. Sup. (to appear).
- H. J. Sussmann, Real analytic desingularization and subanalytic sets: an elementary approach, Trans. Amer. Math. Soc. 317 (1990), no. 2, 417–461. MR 943608, DOI 10.1090/S0002-9947-1990-0943608-5
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 344 (1994), 583-595
- MSC: Primary 32B20
- DOI: https://doi.org/10.1090/S0002-9947-1994-1160156-4
- MathSciNet review: 1160156