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Semianalytic and subanalytic sets

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Bibliography

  1. E. Bierstone, Differentiable functions,Bol. Soc. Brasil Mat.,11 (1980), 139–180.

    Article  MATH  Google Scholar 

  2. E. Bierstone andP. D. Milman, Algebras of composite differentiable functions,Proc. Sympos. Pure Math.,40, Part 1 (1983), 127–136.

    Google Scholar 

  3. P. J. Cohen, Decision procedures for real andp-adic fields,Comm. Pure Appl. Math.,22 (1969), 131–151.

    Article  MATH  Google Scholar 

  4. M. Coste, Ensembles semi-algébriques, Géométrie algébrique réelle et formes quadratiques (Proceedings, Rennes, 1981),Lecture Notes in Math., No. 959, Berlin-Heidelberg-New York, Springer, 1982, p. 109–138.

    Book  Google Scholar 

  5. J. Denef andL. van den Dries,p-adic and real subanalytic sets,Ann. of Math. (2) (to appear).

  6. Z. Denkowska, S. Łojasiewicz andJ. Stasica, Certaines propriétés élémentaires des ensembles sous-analytiques.Bull. Acad. Polon. Sci. Sér. Sci. Math.,27 (1979), 529–536.

    MATH  Google Scholar 

  7. Z. Denkowska, S. Łojasiewicz andJ. Stasica, Sur le théorème du complémentaire pour les ensembles sous-analytiques,Bull. Acad. Polon. Sci. Sér. Sci. Math.,27 (1979), 537–539.

    MATH  Google Scholar 

  8. Z. Denkowska, S. Łojasiewicz andJ. Stasica, Sur le nombre des composantes connexes de la section d’un sous-analytique,Bull. Acad. Polon. Sci. Sér. Sci. Math.,30 (1982), 333–335.

    MATH  Google Scholar 

  9. Z. Denkowska andJ. Stasica,Ensembles sous-analytiques à la polonaise (preprint, 1985).

  10. G. Efroymson, Substitution in Nash functions,Pacific J. Math.,63 (1976), 137–145.

    MATH  Google Scholar 

  11. A. M. Gabrielov, Projections of semi-analytic sets,Functional Anal. Appl.,2 (1968), 282–291 =Funkcional. Anal. i Prilozen. 2, No. 4 (1968), 18–30.

    Article  MATH  Google Scholar 

  12. A. M. Gabrielov, Formal relations between analytic functions,Math. USSR Izvestija,7 (1973), 1056–1088 =Izv. Akad. Nauk SSSR Ser. Mat.,37 (1973), 1056–1090.

    Article  Google Scholar 

  13. R. M. Hardt, Stratification of real analytic mappings and images,Invent. Math.,28 (1975), 193–208.

    Article  MATH  Google Scholar 

  14. R. M. Hardt, Triangulation of subanalytic sets and proper light subanalytic maps,Invent. Math.,38 (1977), 207–217.

    Article  MATH  Google Scholar 

  15. R. M. Hardt, Some analytic bounds for subanalytic sets,Differential Geometric Control Theory, Boston, Birkhäuser, 1983, p. 259–267.

    Google Scholar 

  16. H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero: I, II,Ann. of Math. (2),79 (1964), 109–326.

    Article  Google Scholar 

  17. H. Hironaka, Subanalytic sets,Number Theory, Algebraic Geometry and Commutative Algebra, Tokyo, Kinokuniya, 1973, p. 453–493.

    Google Scholar 

  18. H. Hironaka,Introduction to real-analytic sets and real-analytic maps, Istituto Matematico “L. Tonelli”, Pisa, 1973.

    Google Scholar 

  19. S. Łojasiewicz, Sur le problème de la division,Studia Math.,8 (1959), 87–136.

    Google Scholar 

  20. S. Łojasiewicz, Triangulation of semi-analytic sets,Ann. Scuola Norm. Sup. Pisa (3),18 (1964), 449–474.

    Google Scholar 

  21. S. Łojasiewicz,Ensembles semi-analytiques, Inst. Hautes Études Sci., Bures-sur-Yvette, 1964.

    Google Scholar 

  22. S. Łojasiewicz, Sur la semi-analyticité des images inverses par l’application-tangente,Bull. Acad. Polon. Sci. Sér. Sci. Math.,27 (1979), 525–527.

    Google Scholar 

  23. B. Malgrange, Frobenius avec singularités, 2. Le cas général,Invent. Math.,39 (1977), 67–89.

    Article  MATH  Google Scholar 

  24. R. Narasimhan, Introduction to the theory of analytic spaces,Lecture Notes in Math., No. 25, Berlin-Heidelberg-New York, Springer, 1966.

    MATH  Google Scholar 

  25. J.-B. Poly andG. Raby, Fonction distance et singularités,Bull. Sci. Math. (2),108 (1984), 187–195.

    MATH  Google Scholar 

  26. M. Tamm, Subanalytic sets in the calculus of variations,Acta Math.,146 (1981), 167–199.

    Article  MATH  Google Scholar 

  27. H. Whitney, Local properties of analytic varieties,Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton, Princeton Univ. Press, 1965, p. 205–244.

    Google Scholar 

  28. O. Zariski, Local uniformization theorem on algebraic varieties,Ann. of Math. (2),41 (1940), 852–896.

    Article  Google Scholar 

  29. O. Zariski andP. Samuel,Commutative Algebra, Vol. II, Berlin-Heidelberg-New York, Springer, 1975.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Canada

    Edward Bierstone & Pierre D. Milman

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  1. Edward Bierstone
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  2. Pierre D. Milman
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Additional information

Dedicated to Stanislaw Łojasiewicz for his sixtieth birthday.

Research partially supported by NSERC operating grant A9070.

Research partially supported by NSERC operating grant A8849.

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Bierstone, E., Milman, P.D. Semianalytic and subanalytic sets. Publications Mathématiques de L’Institut des Hautes Scientifiques 67, 5–42 (1988). https://doi.org/10.1007/BF02699126

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  • DOI: https://doi.org/10.1007/BF02699126

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