000			03880nmm a22002415i 4500
005			20230705150652.0
008			130723s1998 gw | s |||| 0|eng d
020			_a9783662037188 _9978-3-662-03718-8
082			_a516.35 _223
100			_aBochnak, Jacek. _921267
245			_aReal Algebraic Geometry _h[electronic resource] / _cby Jacek Bochnak, Michel Coste, Marie-Francoise Roy.
250			_a1st ed. 1998.
260			_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1998.
300			_aX, 430 p. _bonline resource.
505			_a1. 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.
520			_aThe 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. . . . . . . . . . . . . . . . . .
650			_aAlgebraic geometry. _921268
650			_aAlgebraic Geometry. _921269
700			_aCoste, Michel. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _921270
700			_aRoy, Marie-Francoise. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _921271
856			_uhttps://doi.org/10.1007/978-3-662-03718-8
942			_cEBK
999			_c13736 _d13736