Real Algebraic Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1998
|
| Ausgabe: | 3. Folge |
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics
36 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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. . . . . . . . . . . . . . . . . |
| Beschreibung: | 1 Online-Ressource (X, 430 p) |
| ISBN: | 9783662037188 9783642084294 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-662-03718-8 |
Internformat
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| 490 | 0 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics |v 36 |x 0071-1136 | |
| 500 | |a 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. . . . . . . . . . . . . . . . . . . . . . . . | ||
| 500 | |a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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. | ||
| 500 | |a 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 | 4 | |a Mathematics | |
| 650 | 4 | |a Geometry, algebraic | |
| 650 | 4 | |a Algebraic Geometry | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Reelle algebraische Geometrie |0 (DE-588)4192004-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804153098795483136 |
|---|---|
| any_adam_object | |
| author | Bochnak, Jacek 1943- |
| author_GND | (DE-588)120268256 (DE-588)12026823X (DE-588)120268221 |
| author_facet | Bochnak, Jacek 1943- |
| author_role | aut |
| author_sort | Bochnak, Jacek 1943- |
| author_variant | j b jb |
| building | Verbundindex |
| bvnumber | BV042423277 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184504993 (DE-599)BVBBV042423277 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-03718-8 |
| edition | 3. Folge |
| format | Electronic eBook |
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| id | DE-604.BV042423277 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662037188 9783642084294 |
| issn | 0071-1136 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858694 |
| oclc_num | 1184504993 |
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| physical | 1 Online-Ressource (X, 430 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1998 |
| publishDateSearch | 1998 |
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| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics |
| spelling | Bochnak, Jacek 1943- Verfasser (DE-588)120268256 aut Real Algebraic Geometry by Jacek Bochnak, Michel Coste, Marie-Françoise Roy 3. Folge Berlin, Heidelberg Springer Berlin Heidelberg 1998 1 Online-Ressource (X, 430 p) txt rdacontent c rdamedia cr rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete / A Series of Modern Surveys in Mathematics 36 0071-1136 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. . . . . . . . . . . . . . . . . Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Reelle algebraische Geometrie (DE-588)4192004-1 gnd rswk-swf Reelle algebraische Geometrie (DE-588)4192004-1 s 1\p DE-604 Algebraische Geometrie (DE-588)4001161-6 s 2\p DE-604 Coste, Michel 1950- Sonstige (DE-588)12026823X oth Roy, Marie-Françoise 1950- Sonstige (DE-588)120268221 oth https://doi.org/10.1007/978-3-662-03718-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bochnak, Jacek 1943- Real Algebraic Geometry Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd Reelle algebraische Geometrie (DE-588)4192004-1 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4192004-1 |
| title | Real Algebraic Geometry |
| title_auth | Real Algebraic Geometry |
| title_exact_search | Real Algebraic Geometry |
| title_full | Real Algebraic Geometry by Jacek Bochnak, Michel Coste, Marie-Françoise Roy |
| title_fullStr | Real Algebraic Geometry by Jacek Bochnak, Michel Coste, Marie-Françoise Roy |
| title_full_unstemmed | Real Algebraic Geometry by Jacek Bochnak, Michel Coste, Marie-Françoise Roy |
| title_short | Real Algebraic Geometry |
| title_sort | real algebraic geometry |
| topic | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd Reelle algebraische Geometrie (DE-588)4192004-1 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie Reelle algebraische Geometrie |
| url | https://doi.org/10.1007/978-3-662-03718-8 |
| work_keys_str_mv | AT bochnakjacek realalgebraicgeometry AT costemichel realalgebraicgeometry AT roymariefrancoise realalgebraicgeometry |