Book Review

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Book Information:

Author: M. Shiota

Title: Geometry of subanalytic and semialgebraic sets

Additional book information: Birkhäuser, Boston, MA, 1997, xii+431 pp., ISBN 0-8176-4000-2, $89.50$

**[Co]**

*Topological Types of Fewnomials*. Singularities Symposium - {\L}ojasiewicz 70. Banach Center Pub. 44, Polish Acad. Sci. (1998), 81-92. CMP

**99:09**

**[vdD]**

*Tame Topology and O-minimal Structures*. London Math. Soc. Lect. Notes 248. Cambridge Univ. Press 1998. CMP

**98:15**

*Geometric categories and o-minimal structures*, Duke Math. J.

**84**(1996), no. 2, 497–540. MR

**1404337**, DOI 10.1215/S0012-7094-96-08416-1

*Topological stability of smooth mappings*, Lecture Notes in Mathematics, Vol. 552, Springer-Verlag, Berlin-New York, 1976. MR

**0436203**

*Definable sets in ordered structures. I*, Trans. Amer. Math. Soc.

**295**(1986), no. 2, 565–592. MR

**833697**, DOI 10.1090/S0002-9947-1986-0833697-X

*Elementary differential topology*, Annals of Mathematics Studies, No. 54, Princeton University Press, Princeton, N.J., 1963. Lectures given at Massachusetts Institute of Technology, Fall, 1961. MR

**0163320**

**[PeSt]**

*A Trichotomy Theorem for O-minimal Structures*. Proc. London Math. Soc. 77 (1998), 481-523. CMP

**99:01**

*Definable sets in ordered structures. I*, Trans. Amer. Math. Soc.

**295**(1986), no. 2, 565–592. MR

**833697**, DOI 10.1090/S0002-9947-1986-0833697-X

*Nash manifolds*, Lecture Notes in Mathematics, vol. 1269, Springer-Verlag, Berlin, 1987. MR

**904479**, DOI 10.1007/BFb0078571

**[Sh2]**

*Thom's Conjecture on Triangulation of Maps*. Sûrikaisekikenkyûsho Kôkyûroku No. 1050 (1998), 12-28. CMP

**99:09**

*Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function*, J. Amer. Math. Soc.

**9**(1996), no. 4, 1051–1094. MR

**1398816**, DOI 10.1090/S0894-0347-96-00216-0

**[Wi2]**

*A General Theorem of the Complement and Some New O-minimal Structures*. Preprint, 1996.

Review Information:

Reviewer: Michel Coste

Affiliation: University of Rennes

Email: coste@univ-rennes1.fr

Journal: Bull. Amer. Math. Soc.

**36**(1999), 523-527

DOI: https://doi.org/10.1090/S0273-0979-99-00793-4

Published electronically: July 27, 1999

Review copyright: © Copyright 1999 American Mathematical Society