Models for smooth infinitesimal analysis:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1991
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 395 - 399 |
| Physical Description: | X, 399 S. |
| ISBN: | 354097489X 038797489X |
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MARC
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| 245 | 1 | 0 | |a Models for smooth infinitesimal analysis |c Ieke Moerdijk ; Gonzalo E. Reyes |
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Record in the Search Index
| _version_ | 1804118548488912896 |
|---|---|
| adam_text | Contents
Preface v
Introduction 1
I C°° Rings 15
1 C°° Rings 15
2 Manifolds as 7°° rings 24
3 Local C°° rings 31
4 Appendix: Real Closed Rings and Weil Algebras .... 40
5 Ideals of Smooth Functions 44
II C°° Rings as Variable Spaces 57
1 The Category L of Loci 58
2 Smooth Functors as a Basis for Synthetic Calculus . . 71
3 Some Topological Properties of the Smooth Line .... 87
m Two Archimedean Models for Synthetic Calculus 97
1 The Topos £ of Germ Determined Ideals and its Logic 98
2 The topos 7 of closed ideals 112
3 The Topology of Manifolds in 7 and $ 120
IV Cohomology and Integration 133
1 De Rham Cohomology 134
2 Singular Homology 148
3 De Rham s Theorem in 7 and Q 155
4 From Synthetic to Classical Analysis 166
5 Appendix: Weil s Version of De Rham s Theorem . . . 176
V Connections on Microlinear Spaces 181
1 Microlinear Spaces 182
2 Connections and Sprays on a Microlinear Space . . . .189
3 Vector Bundles and Vector Fields 195
4 The Tangent Bundle of a Microlinear Space 202
5 The Gauss Bonnet Theorem in Dimension 2 213
6 Ehresmann Connections on a Principal Fiber Bundle . 219
7 Back to Classical Manifolds 226
Contents x
VI Models with Invertible Infinitesimals 239
1 A Smooth Version of the Zariski Topos 241
2 Smooth Integers 248
3 Manifolds in the Smooth Zariski Topos 261
4 The Degree of a Map 280
5 Forcing the Existence of Invertible Infinitesimals .... 285
VII Smooth Infinitesimal Analysis 293
1 An Axiomatic System for Smooth Infinitesimal Analysis294
2 Some Elementary Mathematical Consequences 302
3 Invertible Infinitesimals and Distributions 320
4 A Transfer Principle Between the Models B and $ . . . 337
Appendix 1: Sheaves and Forcing 345
1 Sites 345
2 Sheaves 347
3 Forcing 353
Appendix 2: A survey of models 363
Appendix 3: The integration axiom 369
Appendix 4: The amazing right adjoint 375
Appendix 5: Comments, References and Further Devel¬
opments 377
Index 387
Index of symbols 391
Bibliography 395
|
| any_adam_object | 1 |
| author | Moerdijk, Ieke Reyes, Gonzalo E. 1937- |
| author_GND | (DE-588)108794997 |
| author_facet | Moerdijk, Ieke Reyes, Gonzalo E. 1937- |
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| author_variant | i m im g e r ge ger |
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| ctrlnum | (OCoLC)246510580 (DE-599)BVBBV004367811 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004367811 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:12:03Z |
| institution | BVB |
| isbn | 354097489X 038797489X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002711985 |
| oclc_num | 246510580 |
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| physical | X, 399 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| spelling | Moerdijk, Ieke Verfasser aut Models for smooth infinitesimal analysis Ieke Moerdijk ; Gonzalo E. Reyes New York u.a. Springer 1991 X, 399 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 395 - 399 Glatte Infinitesimalanalysis (DE-588)4253448-3 gnd rswk-swf Glatte Infinitesimalanalysis (DE-588)4253448-3 s DE-604 Reyes, Gonzalo E. 1937- Verfasser (DE-588)108794997 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002711985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moerdijk, Ieke Reyes, Gonzalo E. 1937- Models for smooth infinitesimal analysis Glatte Infinitesimalanalysis (DE-588)4253448-3 gnd |
| subject_GND | (DE-588)4253448-3 |
| title | Models for smooth infinitesimal analysis |
| title_auth | Models for smooth infinitesimal analysis |
| title_exact_search | Models for smooth infinitesimal analysis |
| title_full | Models for smooth infinitesimal analysis Ieke Moerdijk ; Gonzalo E. Reyes |
| title_fullStr | Models for smooth infinitesimal analysis Ieke Moerdijk ; Gonzalo E. Reyes |
| title_full_unstemmed | Models for smooth infinitesimal analysis Ieke Moerdijk ; Gonzalo E. Reyes |
| title_short | Models for smooth infinitesimal analysis |
| title_sort | models for smooth infinitesimal analysis |
| topic | Glatte Infinitesimalanalysis (DE-588)4253448-3 gnd |
| topic_facet | Glatte Infinitesimalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002711985&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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