Dimension and extensions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
North-Holland
1993
|
| Series: | North-Holland mathematical library
48 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 331 S. Ill. |
| ISBN: | 0444897402 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Preface vii
Chapter I. The separable case in historical
perspective 1
1.1. A compactification problem 1
1.2. Dimensionsgrad 2
1.3. The small inductive dimension ind 3
1.4. The large inductive dimension Ind 9
1.5. The compactness degree; de Groot s prob¬
lem 14
1.6. Splitting the compactification problem 20
1.7. The completeness degree 28
1.8. The covering dimension dim 41
1.9. The covering completeness degree 48
1.10. The CT compactness degree 53
1.11. Pol s example 59
1.12. Kimura s theorem 66
1.13. Guide to dimension theory 68
1.14. Historical comments and unsolved problems 69
Chapter II. Mappings into spheres 73
II. 1. Classes and universe 74
11.2. Inductive dimension modulo a class V 76
11.3. Kernels and surplus 85
11.4. P Ind and mappings into spheres 87
11.5. Covering dimensions modulo a class V 93
11.6. P dim and mappings into spheres 100
11.7. Comparison of TMnd and P dim 106
11.8. Hulls and deficiency 109
11.9. Absolute Borel classes in metric spaces 112
11.10. Dimension modulo Borel classes 119
xi
xii CONTENTS
11.11. Historical comments and unsolved problems 126
Chapter III. Functions of inductive dimen¬
sional type 129
111.1. Additivity 130
111.2. Normal families 139
111.3. Optimal universe 146
111.4. Embedding theorems 160
111.5. Axioms for the dimension function 171
111.6. Historical comments and unsolved problems 181
Chapter IV. Functions of covering dimen¬
sional type 185
IV. 1. Finite unions 186
IV.2. Normal families 192
IV.3. The Dowker universe V 197
IV.4. Dimension and mappings 204
IV.5. Historical comments and unsolved problems 215
Chapter V. Functions of basic dimensional
type 217
V.I. The basic inductive dimension 217
V.2. Excision and extension 223
V.3. The order dimension 234
V.4. The mixed inductive dimension 241
V.5. Historical comments and unsolved problems 244
Chapter VI. Compactifications 247
VI. 1. Wallman compactifications 248
VI.2. Dimension preserving compactifications 258
VI.3. The Freudenthal compactification 266
VI.4. The inequality £ Ind /C Def 282
VI.5. Kimura s characterization of /C def 287
VI.6. The inequality /C dim /C def 300
VI.7. Historical comments and unsolved problems 312
Chart 1. The absolute Borel classes 72
Chart 2. Compactness dimension functions 246
Bibliography 315
List of symbols 327
Index 329
|
| any_adam_object | 1 |
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| author_sort | Aarts, J. M. 1938-2018 |
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| id | DE-604.BV006618559 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:49:21Z |
| institution | BVB |
| isbn | 0444897402 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004229370 |
| oclc_num | 246747901 |
| open_access_boolean | |
| owner | DE-12 DE-634 DE-11 DE-188 |
| owner_facet | DE-12 DE-634 DE-11 DE-188 |
| physical | XII, 331 S. Ill. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | North-Holland |
| record_format | marc |
| series | North-Holland mathematical library |
| series2 | North-Holland mathematical library |
| spelling | Aarts, J. M. 1938-2018 Verfasser (DE-588)1077023162 aut Dimension and extensions J. M. Aarts ; T. Nishiura Amsterdam [u.a.] North-Holland 1993 XII, 331 S. Ill. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 48 Kompaktifizierung (DE-588)4164859-6 gnd rswk-swf Dimensionstheorie (DE-588)4149935-9 gnd rswk-swf Kompaktifizierung (DE-588)4164859-6 s DE-604 Dimensionstheorie (DE-588)4149935-9 s Nishiura, Togo 1931- Verfasser (DE-588)172573270 aut North-Holland mathematical library 48 (DE-604)BV000005206 48 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004229370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Aarts, J. M. 1938-2018 Nishiura, Togo 1931- Dimension and extensions North-Holland mathematical library Kompaktifizierung (DE-588)4164859-6 gnd Dimensionstheorie (DE-588)4149935-9 gnd |
| subject_GND | (DE-588)4164859-6 (DE-588)4149935-9 |
| title | Dimension and extensions |
| title_auth | Dimension and extensions |
| title_exact_search | Dimension and extensions |
| title_full | Dimension and extensions J. M. Aarts ; T. Nishiura |
| title_fullStr | Dimension and extensions J. M. Aarts ; T. Nishiura |
| title_full_unstemmed | Dimension and extensions J. M. Aarts ; T. Nishiura |
| title_short | Dimension and extensions |
| title_sort | dimension and extensions |
| topic | Kompaktifizierung (DE-588)4164859-6 gnd Dimensionstheorie (DE-588)4149935-9 gnd |
| topic_facet | Kompaktifizierung Dimensionstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004229370&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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