Synthetic differential geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | London Mathematical Society lecture note series
333 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 233 S. graph. Darst. |
| ISBN: | 0521687381 9780521687386 |
Internformat
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Datensatz im Suchindex
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| adam_text | LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES: 333 SYNTHETIC
DIFFERENTIAL GEOMETRY 2 ND EDITION ANDERS KOCK AARHUS UNIVERSITY,
DENMARK CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE TO THE SECOND
EDITION (2006) PAGE VII PREFACE TO THE FIRST EDITION (1981) IX I THE
SYNTHETIC THEORY 1 1.1 BASIC STRUCTURE ON THE GEOMETRIC LINE 2 1.2
DIFFERENTIAL CALCULUS 6 1.3 HIGHER TAYLOR FORMULAE (ONE VARIABLE) 9 1.4
PARTIAL DERIVATIVES 12 1.5 HIGHER TAYLOR FORMULAE IN SEVERAL VARIABLES.
TAYLOR SERIES 15 1.6 SOME IMPORTANT INFINITESIMAL OBJECTS * 18 1.7
TANGENT VECTORS AND THE TANGENT BUNDLE 23 1.8 VECTOR FIELDS AND
INFINITESIMAL TRANSFORMATIONS 28 1.9 LIE BRACKET - COMMUTATOR OF
INFINITESIMAL TRANSFOR- MATIONS 32 1.10 DIRECTIONAL DERIVATIVES 36 1.11
FUNCTIONAL ANALYSIS. APPLICATION TO PROOF OF JACOBI IDENTITY 40 1.12 THE
COMPREHENSIVE AXIOM 43 1.13 ORDER AND INTEGRATION 48 1.14 FORMS AND
CURRENTS 52 1.15 CURRENTS DEFINED USING INTEGRATION. STOKES THEOREM 58
1.16 WEIL ALGEBRAS .61 1.17 FORMAL MANIFOLDS . 68 1.18 DIFFERENTIAL
FORMS IN TERMS OF SIMPLICES 75 1.19 OPEN COVERS 82 1.20 DIFFERENTIAL
FORMS AS QUANTITIES 87 1.21 PURE GEOMETRY 90 VI CONTENTS II CATEGORICAL
LOGIC 97 II. 1 GENERALIZED ELEMENTS 98 11.2 SATISFACTION (1) 99 11.3
EXTENSIONS AND DESCRIPTIONS 103 11.4 SEMANTICS OF FUNCTION OBJECTS 108
II. 5 AXIOM 1 REVISITED 113 11.6 COMMA CATEGORIES 115 11.7 DENSE CLASS
OF GENERATORS 121 11.8 SATISFACTION (2) 123 11.9 GEOMETRIC THEORIES 127
III MODELS 131 111.1 MODELS FOR AXIOMS 1, 2, AND 3 131 111.2 MODELS FOR
E-STABLE GEOMETRIC THEORIES 138 111.3 AXIOMATIC THEORY OF WELL-ADAPTED
MODELS (1) 143 111.4 AXIOMATIC THEORY OF WELL-ADAPTED MODELS (2) 148
111.5 THE ALGEBRAIC THEORY OF SMOOTH FUNCTIONS 154 111.6 GERM-DETERMINED
TF^-ALGEBRAS 164 111.7 THE OPEN COVER TOPOLOGY 170 111.8 CONSTRUCTION OF
WELL-ADAPTED MODELS 175 111.9 W-DETERMINED ALGEBRAS, AND MANIFOLDS WITH
BOUNDARY 181 III. 10 A FIELD PROPERTY OF R AND THE SYNTHETIC ROLE OF
GERM ALGEBRAS 192 III. 11 ORDER AND INTEGRATION IN THE CAHIERS TOPOS 198
APPENDICES 207 BIBLIOGRAPHY 223 INDEX 231
|
| adam_txt |
LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES: 333 SYNTHETIC
DIFFERENTIAL GEOMETRY 2 ND EDITION ANDERS KOCK AARHUS UNIVERSITY,
DENMARK CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE TO THE SECOND
EDITION (2006) PAGE VII PREFACE TO THE FIRST EDITION (1981) IX I THE
SYNTHETIC THEORY 1 1.1 BASIC STRUCTURE ON THE GEOMETRIC LINE 2 1.2
DIFFERENTIAL CALCULUS 6 1.3 HIGHER TAYLOR FORMULAE (ONE VARIABLE) 9 1.4
PARTIAL DERIVATIVES 12 1.5 HIGHER TAYLOR FORMULAE IN SEVERAL VARIABLES.
TAYLOR SERIES 15 1.6 SOME IMPORTANT INFINITESIMAL OBJECTS * 18 1.7
TANGENT VECTORS AND THE TANGENT BUNDLE 23 1.8 VECTOR FIELDS AND
INFINITESIMAL TRANSFORMATIONS 28 1.9 LIE BRACKET - COMMUTATOR OF
INFINITESIMAL TRANSFOR- MATIONS 32 1.10 DIRECTIONAL DERIVATIVES 36 1.11
FUNCTIONAL ANALYSIS. APPLICATION TO PROOF OF JACOBI IDENTITY 40 1.12 THE
COMPREHENSIVE AXIOM 43 1.13 ORDER AND INTEGRATION 48 1.14 FORMS AND
CURRENTS 52 1.15 CURRENTS DEFINED USING INTEGRATION. STOKES' THEOREM 58
1.16 WEIL ALGEBRAS .61 1.17 FORMAL MANIFOLDS . 68 1.18 DIFFERENTIAL
FORMS IN TERMS OF SIMPLICES 75 1.19 OPEN COVERS 82 1.20 DIFFERENTIAL
FORMS AS QUANTITIES 87 1.21 PURE GEOMETRY 90 VI CONTENTS II CATEGORICAL
LOGIC 97 II. 1 GENERALIZED ELEMENTS 98 11.2 SATISFACTION (1) 99 11.3
EXTENSIONS AND DESCRIPTIONS 103 11.4 SEMANTICS OF FUNCTION OBJECTS 108
II. 5 AXIOM 1 REVISITED 113 11.6 COMMA CATEGORIES 115 11.7 DENSE CLASS
OF GENERATORS 121 11.8 SATISFACTION (2) 123 11.9 GEOMETRIC THEORIES 127
III MODELS 131 111.1 MODELS FOR AXIOMS 1, 2, AND 3 131 111.2 MODELS FOR
E-STABLE GEOMETRIC THEORIES 138 111.3 AXIOMATIC THEORY OF WELL-ADAPTED
MODELS (1) 143 111.4 AXIOMATIC THEORY OF WELL-ADAPTED MODELS (2) 148
111.5 THE ALGEBRAIC THEORY OF SMOOTH FUNCTIONS 154 111.6 GERM-DETERMINED
TF^-ALGEBRAS 164 111.7 THE OPEN COVER TOPOLOGY 170 111.8 CONSTRUCTION OF
WELL-ADAPTED MODELS 175 111.9 W-DETERMINED ALGEBRAS, AND MANIFOLDS WITH
BOUNDARY 181 III. 10 A FIELD PROPERTY OF R AND THE SYNTHETIC ROLE OF
GERM ALGEBRAS 192 III. 11 ORDER AND INTEGRATION IN THE CAHIERS TOPOS 198
APPENDICES 207 BIBLIOGRAPHY 223 INDEX 231 |
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| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 2. ed. |
| format | Book |
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| index_date | 2024-07-02T14:59:41Z |
| indexdate | 2024-07-09T20:40:33Z |
| institution | BVB |
| isbn | 0521687381 9780521687386 |
| language | English |
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| physical | XII, 233 S. graph. Darst. |
| publishDate | 2006 |
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| publisher | Cambridge Univ. Press |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | Kock, Anders 1938- Verfasser (DE-588)132017598 aut Synthetic differential geometry 2. ed. Cambridge [u.a.] Cambridge Univ. Press 2006 XII, 233 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 333 Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s DE-604 London Mathematical Society lecture note series 333 (DE-604)BV000000130 333 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014854688&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kock, Anders 1938- Synthetic differential geometry London Mathematical Society lecture note series Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 |
| title | Synthetic differential geometry |
| title_auth | Synthetic differential geometry |
| title_exact_search | Synthetic differential geometry |
| title_exact_search_txtP | Synthetic differential geometry |
| title_full | Synthetic differential geometry |
| title_fullStr | Synthetic differential geometry |
| title_full_unstemmed | Synthetic differential geometry |
| title_short | Synthetic differential geometry |
| title_sort | synthetic differential geometry |
| topic | Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Geometry, Differential Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014854688&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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