Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Real Algebraic Geometry

Authors: Bochnak, Jacek, Coste, Michel, Roy, Marie-Francoise

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About this book

The present volume is a translation, revision and updating of our book (pub­ lished in French) with the title "Geometrie Algebrique Reelle". Since its pub­ lication in 1987 the theory has made advances in several directions. There have also been new insights into material already in the French edition. Many of these advances and insights have been incorporated in this English version of the book, so that it may be viewed as being substantially different from the original. We wish to thank Michael Buchner for his careful reading of the text and for his linguistic corrections and stylistic improvements. The initial Jb. TEiX file was prepared by Thierry van Effelterre. The three authors participate in the European research network "Real Algebraic and Analytic Geometry". The first author was partially supported by NATO Collaborative Research Grant 960011. Jacek Bochnak April 1998 Michel Coste Marie-Pranroise Roy Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Ordered Fields, Real Closed Fields . . . . . . . . . . . . . . . . . . . . . . . 7 1. 1 Ordered Fields, Real Fields . . . . . " . . . . . . . . . . . . . . . . . . . . . . . 7 1. 2 Real Closed Fields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1. 3 Real Closure of an Ordered Field. . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 4 The Tarski-Seidenberg Principle. . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. Semi-algebraic Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 1 Algebraic and Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . . . . 23 2. 2 Projection of Semi-algebraic Sets. Semi-algebraic Mappings. . 26 2. 3 Decomposition of Semi-algebraic Sets. . . . . . . . . . . . . . . . . . . . . 30 2. 4 Connectedness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2. 5 Closed and Bounded Semi-algebraic Sets. Curve-selection Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2. 6 Continuous Semi-algebraic Functions. Lojasiewicz's Inequality 42 2. 7 Separation of Closed Semi-algebraic Sets. . . . . . . . . . . . . . . . . .

Table of contents (16 chapters)

Buy this book

eBook £87.50
price for United Kingdom (gross)
  • ISBN 978-3-662-03718-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover £109.99
price for United Kingdom (gross)
  • ISBN 978-3-540-64663-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover £109.99
price for United Kingdom (gross)
  • ISBN 978-3-642-08429-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Real Algebraic Geometry
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
36
Copyright
1998
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-03718-8
DOI
10.1007/978-3-662-03718-8
Hardcover ISBN
978-3-540-64663-1
Softcover ISBN
978-3-642-08429-4
Series ISSN
0071-1136
Edition Number
1
Number of Pages
X, 430
Additional Information
Title of the original French edition: Geometrie algebrique reelle: in the series Ergebnisse Mathematik 3. Folge volume 12
Topics