About this product

Product Identifiers

PublisherSpringer Berlin / Heidelberg

ISBN-103540646639

ISBN-139783540646631

eBay Product ID (ePID)637390

Product Key Features

Number of PagesX, 430 Pages

LanguageEnglish

Publication NameReal Algebraic Geometry

SubjectFunctional Analysis, Geometry / Algebraic

Publication Year1998

TypeTextbook

Subject AreaMathematics

AuthorMichel Coste, Jacek Bochnak, M. -F. Roy

SeriesErgebnisse der Mathematik und Ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics Ser.

FormatHardcover

Dimensions

Item Weight62.1 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN98-029344

Dewey Edition21

Reviews"Wie schon das französische Original, so ist auch die englische Version sehr sorgfältig verfasst. Beim Vergleich zwischen beiden stösst man immer wieder auf Stellen, wo der ursprüngliche Text nicht nur einfach übersetzt, sondern im Interesse einer noch klareren Darstellung auch neu konzipiert worden ist. Kein Zweifel, dass die neue Fassung auch weiterhin die Rolle einer Standradreferenz spielen wird."DMV Jahresbericht, 103. Band, Heft 2, Juli 2001, "Wie schon das franzsische Original, so ist auch die englische Version sehr sorgfltig verfasst. Beim Vergleich zwischen beiden stsst man immer wieder auf Stellen, wo der ursprngliche Text nicht nur einfach bersetzt, sondern im Interesse einer noch klareren Darstellung auch neu konzipiert worden ist. Kein Zweifel, dass die neue Fassung auch weiterhin die Rolle einer Standradreferenz spielen wird." DMV Jahresbericht, 103. Band, Heft 2, Juli 2001, "Wie schon das französische Original, so ist auch die englische Version sehr sorgfältig verfasst. Beim Vergleich zwischen beiden stösst man immer wieder auf Stellen, wo der ursprüngliche Text nicht nur einfach übersetzt, sondern im Interesse einer noch klareren Darstellung auch neu konzipiert worden ist. Kein Zweifel, dass die neue Fassung auch weiterhin die Rolle einer Standradreferenz spielen wird." DMV Jahresbericht, 103. Band, Heft 2, Juli 2001

Series Volume Number36

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal516.3/5

Table Of Content1. 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.

SynopsisThe 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. . . . . . . . . . . . . . . . . ., 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. . . . . . . . . . . . . . . . . ., The present volume is a translation, revision and updating of our book (published in French) with the title "Géométrie Algébrique Réelle". Since its publication 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., This book is a systematic treatment of real algebraic geometry. It is carefully and clearly written; it starts with the basic concepts and leads to up-to-date research topics. The present volume is a translation, revision and updating of ERGEBNISSE vol.12, published in French in 1987. Many new developments in this field have been included in this book.

LC Classification NumberQA564-609