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Catalogue Information
Field name	Details
Dewey Class	516.35
Title	Real Algebraic Geometry ([EBook] /) / by Jacek Bochnak, Michel Coste, Marie-Françoise Roy.
Author	Bochnak, Jacek
Added Personal Name	Coste, Michel author.
Added Personal Name	Roy, Marie-Françoise author.
Other name(s)	SpringerLink (Online service)
Edition statement	3. Folge.
Publication	Berlin, Heidelberg : : Springer Berlin Heidelberg : : Imprint: Springer, , 1998.
Physical Details	X, 430 p. : online resource.
Series	Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics 0071-1136 ; ; 36
ISBN	9783662037188
Summary Note	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. . . . . . . . . . . . . . . . . .:
Contents note	1. Ordered Fields, Real Closed Fields -- 2. Semi-algebraic Sets -- 3. Real Algebraic Varieties -- 4. Real Algebra -- 5. The Tarski-Seidenberg Principle as a Transfer Tool -- 6. Hilbert’s 17th Problem. Quadratic Forms -- 7. Real Spectrum -- 8. Nash Functions -- 9. Stratifications -- 10. Real Places -- 11. Topology of Real Algebraic Varieties -- 12. Algebraic Vector Bundles -- 13. Polynomial or Regular Mappings with Values in Spheres -- 14. Algebraic Models of C? Manifolds -- 15. Witt Rings in Real Algebraic Geometry -- Index of Notation.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-662-03718-8
Links to Related Works	Subject References: Algebraic Geometry . Mathematics . Authors: Bochnak, Jacek . Coste, Michel . Roy, Marie-Françoise . Corporate Authors: SpringerLink (Online service) . Series: Ergebnisse der Mathematik und ihrer Grenzgebiete, A Series of Modern Surveys in Mathematics . Classification: 516.35 .

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Real Algebraic Geometry

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