On strong C0-equivalence of real analytic functions

Satoshi KOIKE

doi:10.2969/jmsj/04520313

On strong C⁰-equivalence of real analytic functions

Satoshi KOIKE

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JOURNAL FREE ACCESS

1993 Volume 45 Issue 2 Pages 313-320

DOI https://doi.org/10.2969/jmsj/04520313

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Published: 1993 Received: September 17, 1991 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. Briancon and J.P. Speder, La trivialité topologique n'implique pas les conditions de Whitney, C.R. Acad. Sci. Paris, 280 (1975), 365-367.
2) M.A. Buchner and W. Kucharz, Almost analytic local algebraicity of analytic sets and functions, Math. Z., 196 (1987), 65-74.
3) T. Fukui, The modified analytic trivialization of a family of real analytic mappings, Contemporary Math., 90 (1989), 73-89.
4) T. Fukui, The modified analytic trivialization via the weighted blowing up, J. Math. Soc. Japan, 44 (1992), 455-459.
5) T. Fukui and E. Yoshinaga, The modified analytic trivialization of family of real analytic functions, Invent. Math., 82 (1985), 467-477.
6) W. Kucharz, Global almost analytic algebraicity of analytic sets, Pacific J. Math., 143 (1990), 287-300.
7) T.C. Kuo, Une classification des singularités réelles, C.R. Acad. Sci. Paris, 288 (1979), 809-812.
8) T.C. Kuo, The modified analytic trivialization of singularities, J. Math. Soc. Japan, 32 (1980), 605-614.
9) T.C. Kuo, On classification of real singularities, Invent. Math., 82 (1985), 257-262.
10) T.C. Kuo, A natural equivalence relation on singularities, Singularities, Banach Center Publ., 20 (1988), 239-243.
11) T.C. Kuo, Some ideas of Thom and their outcome, preprint.
12) T.C. Kuo and J.N. Ward, A theorem on almost analytic equisingularities, J. Math. Soc. Japan, 33 (1981), 471-484.
13) H.B. Laufer, Weak simultaneous resolution for deformations of Gorenstein surface singularities, Proc. Sympos. Pure Math., 40 part 2 (1983), 1-29.
14) H.B. Laufer, Strong simultaneous resolution for surface singularities, Adv. Stud. Pure Math., 8 (1986), 207-214.
15) M. Oka, On the weak simultaneous resolution of a negligible truncation of the Newton boundary, Contemporary Math., 90 (1989), 199-210.
16) M. Suzuki, Stability of Newton boundaries of a family of real analytic singularities, Trans. Amer. Math. Soc., 323 (1991), 133-150.
17) B. Teissier, Resolution simultanée I, II, Seminaire sur les Singularités des Surfaces, Lect. Notes in Math., 777, Springer-Verlag, 1980, pp. 71-146.
18) E. Yoshinaga, The modified analytic trivialization of real analytic families via blowing-ups, J. Math. Soc. Japan, 40 (1988), 161-179.

Right : [1] J. Briançon and J. P. Speder, La trivialité topologique n'implique pas les conditions de Whitney, C. R. Acad. Sci. Paris, 280 (1975), 365-367.
[2] M.A. Buchner and W. Kucharz, Almost analytic local algebraicity of analytic sets and functions, Math. Z., 196 (1987), 65-74.
[3] T. Fukui, The modified analytic trivialization of a family of real analytic mappings, Contemporary Math., 90 (1989), 73-89.
[4] T. Fukui, The modified analytic trivialization via the weighted blowing up, J. Math. Soc. Japan, 44 (1992), 455-459.
[5] T. Fukui and E. Yoshinaga, The modified analytic trivialization of family of real analytic functions, Invent. Math., 82 (1985), 467-477.
[6] W. Kucharz, Global almost analytic algebraicity of analytic sets, Pacific J. Math., 143 (1990), 287-300.
[7] T. C. Kuo, Une classification des singularités réelles, C. R. Acad. Sci. Paris, 288 (1979), 809-812.
[8] T. C. Kuo, The modified analytic trivialization of singularities, J. Math. Soc. Japan, 32 (1980), 605-614.
[9] T. C. Kuo, On classification of real singularities, Invent. Math., 82 (1985), 257-262.
[10] T. C. Kuo, A natural equivalence relation on singularities, Singularities, Banach Center Publ., 20 (1988), 239-243.
[11] T. C. Kuo, Some ideas of Thom and their outcome, preprint.
[12] T. C. Kuo and J. N. Ward, A theorem on almost analytic equisingularities, J. Math. Soc. Japan, 33 (1981), 471-484.
[13] H. B. Laufer, Weak simultaneous resolution for deformations of Gorenstein surface singularities, Proc. Sympos. Pure Math., 40 part 2 (1983), 1-29.
[14] H. B. Laufer, Strong simultaneous resolution for surface singularities, Adv. Stud. Pure Math., 8 (1986), 207-214.
[15] M. Oka, On the weak simultaneous resolution of a negligible truncation of the Newton boundary, Contemporary Math., 90 (1989), 199-210.
[16] M. Suzuki, Stability of Newton boundaries of a family of real analytic singularities, Trans. Amer. Math. Soc., 323 (1991), 133-150.
[17] B. Teissier, Resolution simultanée I, II, Seminaire sur les Singularités des Surfaces, Lect. Notes in Math., 777, Springer-Verlag, 1980, pp. 71-146.
[18] E. Yoshinaga, The modified analytic trivialization of real analytic families via blowing-ups, J. Math. Soc. Japan, 40 (1988), 161-179.

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