Foundations of analysis over surreal number fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North-Holland
1987
|
| Schriftenreihe: | North-Holland mathematics studies
141 Notas de matemática (Rio de Janeiro, Brazil) no. 117 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand Includes bibliographical references (p. 353-358) and index |
| Beschreibung: | 1 Online-Ressource (xvi, 373 p.) |
| ISBN: | 9780444702265 0444702261 9780080872520 0080872522 1281798053 9781281798053 |
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| 500 | |a In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Alling, Norman L. 1930- |
| author_GND | (DE-588)142126985 |
| author_facet | Alling, Norman L. 1930- |
| author_role | aut |
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| dewey-full | 510 512/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 512 - Algebra |
| dewey-raw | 510 512/.3 |
| dewey-search | 510 512/.3 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV042317482 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:18:16Z |
| institution | BVB |
| isbn | 9780444702265 0444702261 9780080872520 0080872522 1281798053 9781281798053 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027754473 |
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| physical | 1 Online-Ressource (xvi, 373 p.) |
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| publishDate | 1987 |
| publishDateSearch | 1987 |
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| publisher | North-Holland |
| record_format | marc |
| series2 | North-Holland mathematics studies Notas de matemática (Rio de Janeiro, Brazil) |
| spelling | Alling, Norman L. 1930- Verfasser (DE-588)142126985 aut Foundations of analysis over surreal number fields Norman L. Alling Amsterdam North-Holland 1987 1 Online-Ressource (xvi, 373 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematics studies 141 Notas de matemática (Rio de Janeiro, Brazil) no. 117 In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathematics is brought to bear on the problems at hand Includes bibliographical references (p. 353-358) and index Algebraic number fields Surrealer Zahlkörper swd Nombres surréels Corps algébriques Analyse mathématique Algebraic fields fast Mathematical analysis fast Surreal numbers fast MATHEMATICS / Algebra / Intermediate bisacsh série formelle série puissance espace affine topologie nombre réel Corps algébriques ram Analyse mathématique ram Zahlkörper swd Surreal numbers Algebraic fields Mathematical analysis Zahlkörper (DE-588)4067273-6 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Surreale Zahl (DE-588)4439590-5 gnd rswk-swf Surreale Zahl (DE-588)4439590-5 s Zahlkörper (DE-588)4067273-6 s 1\p DE-604 Analysis (DE-588)4001865-9 s 2\p DE-604 http://www.sciencedirect.com/science/book/9780444702265 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 | Alling, Norman L. 1930- Foundations of analysis over surreal number fields Algebraic number fields Surrealer Zahlkörper swd Nombres surréels Corps algébriques Analyse mathématique Algebraic fields fast Mathematical analysis fast Surreal numbers fast MATHEMATICS / Algebra / Intermediate bisacsh série formelle série puissance espace affine topologie nombre réel Corps algébriques ram Analyse mathématique ram Zahlkörper swd Surreal numbers Algebraic fields Mathematical analysis Zahlkörper (DE-588)4067273-6 gnd Analysis (DE-588)4001865-9 gnd Surreale Zahl (DE-588)4439590-5 gnd |
| subject_GND | (DE-588)4067273-6 (DE-588)4001865-9 (DE-588)4439590-5 |
| title | Foundations of analysis over surreal number fields |
| title_auth | Foundations of analysis over surreal number fields |
| title_exact_search | Foundations of analysis over surreal number fields |
| title_full | Foundations of analysis over surreal number fields Norman L. Alling |
| title_fullStr | Foundations of analysis over surreal number fields Norman L. Alling |
| title_full_unstemmed | Foundations of analysis over surreal number fields Norman L. Alling |
| title_short | Foundations of analysis over surreal number fields |
| title_sort | foundations of analysis over surreal number fields |
| topic | Algebraic number fields Surrealer Zahlkörper swd Nombres surréels Corps algébriques Analyse mathématique Algebraic fields fast Mathematical analysis fast Surreal numbers fast MATHEMATICS / Algebra / Intermediate bisacsh série formelle série puissance espace affine topologie nombre réel Corps algébriques ram Analyse mathématique ram Zahlkörper swd Surreal numbers Algebraic fields Mathematical analysis Zahlkörper (DE-588)4067273-6 gnd Analysis (DE-588)4001865-9 gnd Surreale Zahl (DE-588)4439590-5 gnd |
| topic_facet | Algebraic number fields Surrealer Zahlkörper Nombres surréels Corps algébriques Analyse mathématique Algebraic fields Mathematical analysis Surreal numbers MATHEMATICS / Algebra / Intermediate série formelle série puissance espace affine topologie nombre réel Zahlkörper Analysis Surreale Zahl |
| url | http://www.sciencedirect.com/science/book/9780444702265 |
| work_keys_str_mv | AT allingnormanl foundationsofanalysisoversurrealnumberfields |