Stratifications

  • Jacek Bochnak
  • Michel Coste
  • Marie-Françoise Roy
Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics book series (MATHE3, volume 36)

Abstract

In this chapter, we continue the study of semi-algebraic sets initiated in Chap. 2. In Section 1, we construct stratifications which have a cylindrical structure with respect to all successive projections R k R k-1, which is particularly useful in inductive arguments. In the second section, we prove that a closed and bounded semi-algebraic set can be semi-algebraically triangulated. In Section 3, we investigate the structure of continuous semi-algebraic mappings. As an application, we obtain the theorem of local conic structure of semi-algebraic sets. In Section 4 we prove that a continuous semi-algebraic function is triangulable. We obtain the finiteness of the number of topological types of polynomials in n variables of degree < d. Half-branches of algebraic curves are studied in Section 5. Semi-algebraic versions of Sard’s and Bertini’s theorems are contained in Section 6. The last section is devoted to Whitney’s conditions a and b.

Throughout this chapter, R denotes a real closed field.

Keywords

Manifold Stratification Nash Nite Cylin 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jacek Bochnak
    • 1
  • Michel Coste
    • 2
  • Marie-Françoise Roy
    • 1
  1. 1.Mathematisch InstituutVrije UniversiteitAmsterdamThe Netherlands
  2. 2.Institut Mathématique de RennesUniversité de Rennes 1Rennes cedexFrance

Personalised recommendations