Linear spaces and differentiation theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester u.a.
Wiley
1988
|
| Series: | Pure and applied mathematics.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 234 - 245 |
| Physical Description: | XVI, 246 S. |
| ISBN: | 0471917869 |
Staff View
MARC
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| 100 | 1 | |a Frölicher, Alfred |e Verfasser |0 (DE-588)125936672 |4 aut | |
| 245 | 1 | 0 | |a Linear spaces and differentiation theory |c Alfred Frölicher ; Andreas Kriegl |
| 264 | 1 | |a Chichester u.a. |b Wiley |c 1988 | |
| 300 | |a XVI, 246 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Pure and applied mathematics. | |
| 500 | |a Literaturverz. S. 234 - 245 | ||
| 650 | 7 | |a Bornologie |2 Jussieu | |
| 650 | 7 | |a Calcul différentiel |2 Jussieu | |
| 650 | 4 | |a Calcul infinitésimal | |
| 650 | 7 | |a Calcul infinitésimal |2 ram | |
| 650 | 7 | |a Catégorie |2 Jussieu | |
| 650 | 7 | |a Espace localement convexe |2 Jussieu | |
| 650 | 4 | |a Espaces vectoriels | |
| 650 | 7 | |a Espaces vectoriels |2 ram | |
| 650 | 7 | |a Topologie Mackey |2 Jussieu | |
| 650 | 4 | |a Variétés (Mathématiques) | |
| 650 | 7 | |a Variétés (Mathématiques) |2 ram | |
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Vector spaces | |
| 650 | 0 | 7 | |a Vektorraum |0 (DE-588)4130622-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentiation |g Mathematik |0 (DE-588)4149787-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface ix
1 Foundational Material 1
1.1 Categories generated by a set of maps 2
1.2 Bornologies and / structures 6
1.3 Difference quotients 12
1.4 Lipschitz structures and smooth structures 22
2 Convenient Vector Spaces 27
2.1 Locally convex and convex bornological spaces 28
2.2 The Mackey convergence and the Mackey closure topology 35
2.3 /°° vector spaces and ^^ vector spaces 41
2.4 Preconvenient vector spaces 47
2.5 Separation 52
2.6 Completion 55
3 Multilinear Maps and Categorical Properties 60
3.1 Initial and final structures, categorical completeness 61
3.2 Subspaces and quotients 63
3.3 Products 65
3.4 Coproducts or direct sums 68
3.5 Inductive limits 70
3.6 Function spaces of linear maps 71
3.7 Function spaces of multilinear maps 75
3.8 The tensor product 77
3.9 The duality functor 79
4 Calculus in Convenient Vector Spaces 81
4.1 Differentiable curves 83
4.2 Curve spaces 93
vii
viii Contents
4.3 Differentiable maps 99
4.4 Function spaces and exponential laws 114
4.5 Partial differentiability 134
4.6 Spaces of sections of vector bundles 138
4.7 Certain function spaces are manifolds 145
4.8 Theorems on inverse and implicit functions 151
5 Differentiable Maps and Categorical Properties 154
5.1 Free convenient vector spaces 155
5.2 Convenient co algebfas 165
5.3 Cartesian closed categories of convenient vector spaces 173
5.4 Reflexivity 179
6 The Mackey Closure Topology 188
6.1 Comparison with other topologies 189
6.2 Continuity of the addition and regularity 192
6.3 The Mackey closure of subsets 197
6.4 Convex functions 199
7 Permanence Properties and Counter examples 204
7.1 Extension and lifting properties 205
7.2 Preservation of categorical limits 209
7.3 Preservation of initiality and finality 216
7.4 Various counter examples 221
8 Some Categorical Notions and Notations 224
8.1 Categories 224
8.2 Functors and natural transformations 225
8.3 Limits and colimits 226
8.4 Adjoint functors 228
8.5 Adjoint functors and limits 229
8.6 Cartesian closed categories 229
8.7 Initial sources and final sinks 230
8.8 Embeddings and quotient maps 232
Bibliography 234
List of Symbols 236
List of Categories 239
List of Functors 240
Index 242
|
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002138349 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:40:58Z |
| institution | BVB |
| isbn | 0471917869 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001402362 |
| oclc_num | 16925591 |
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| physical | XVI, 246 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics. |
| spelling | Frölicher, Alfred Verfasser (DE-588)125936672 aut Linear spaces and differentiation theory Alfred Frölicher ; Andreas Kriegl Chichester u.a. Wiley 1988 XVI, 246 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics. Literaturverz. S. 234 - 245 Bornologie Jussieu Calcul différentiel Jussieu Calcul infinitésimal Calcul infinitésimal ram Catégorie Jussieu Espace localement convexe Jussieu Espaces vectoriels Espaces vectoriels ram Topologie Mackey Jussieu Variétés (Mathématiques) Variétés (Mathématiques) ram Calculus Manifolds (Mathematics) Vector spaces Vektorraum (DE-588)4130622-3 gnd rswk-swf Differentiation Mathematik (DE-588)4149787-9 gnd rswk-swf Differentiation Mathematik (DE-588)4149787-9 s Vektorraum (DE-588)4130622-3 s DE-604 Kriegl, Andreas Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001402362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Frölicher, Alfred Kriegl, Andreas Linear spaces and differentiation theory Bornologie Jussieu Calcul différentiel Jussieu Calcul infinitésimal Calcul infinitésimal ram Catégorie Jussieu Espace localement convexe Jussieu Espaces vectoriels Espaces vectoriels ram Topologie Mackey Jussieu Variétés (Mathématiques) Variétés (Mathématiques) ram Calculus Manifolds (Mathematics) Vector spaces Vektorraum (DE-588)4130622-3 gnd Differentiation Mathematik (DE-588)4149787-9 gnd |
| subject_GND | (DE-588)4130622-3 (DE-588)4149787-9 |
| title | Linear spaces and differentiation theory |
| title_auth | Linear spaces and differentiation theory |
| title_exact_search | Linear spaces and differentiation theory |
| title_full | Linear spaces and differentiation theory Alfred Frölicher ; Andreas Kriegl |
| title_fullStr | Linear spaces and differentiation theory Alfred Frölicher ; Andreas Kriegl |
| title_full_unstemmed | Linear spaces and differentiation theory Alfred Frölicher ; Andreas Kriegl |
| title_short | Linear spaces and differentiation theory |
| title_sort | linear spaces and differentiation theory |
| topic | Bornologie Jussieu Calcul différentiel Jussieu Calcul infinitésimal Calcul infinitésimal ram Catégorie Jussieu Espace localement convexe Jussieu Espaces vectoriels Espaces vectoriels ram Topologie Mackey Jussieu Variétés (Mathématiques) Variétés (Mathématiques) ram Calculus Manifolds (Mathematics) Vector spaces Vektorraum (DE-588)4130622-3 gnd Differentiation Mathematik (DE-588)4149787-9 gnd |
| topic_facet | Bornologie Calcul différentiel Calcul infinitésimal Catégorie Espace localement convexe Espaces vectoriels Topologie Mackey Variétés (Mathématiques) Calculus Manifolds (Mathematics) Vector spaces Vektorraum Differentiation Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001402362&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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