Modern dimension theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Heldermann
1983
|
| Ausgabe: | Rev. and extended ed. |
| Schriftenreihe: | Sigma series in pure mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 284 S. |
| ISBN: | 3885380021 |
Internformat
MARC
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| 245 | 1 | 0 | |a Modern dimension theory |c J. Nagata |
| 250 | |a Rev. and extended ed. | ||
| 264 | 1 | |a Berlin |b Heldermann |c 1983 | |
| 300 | |a IX, 284 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Sigma series in pure mathematics |v 2 | |
| 650 | 4 | |a Topologie de l'espace métrique | |
| 650 | 4 | |a Distance geometry | |
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Datensatz im Suchindex
| _version_ | 1804114710888448000 |
|---|---|
| adam_text | CONTENTS
Preface viii
Preface to the Revised Edition ix
Chapter I. Introduction
1.1. Coverings 1
1.2. Metrization 4
1.3. Mappings 7
1.4. Dimension 8
Chapter II. Dimension of metric spaces
11.1. Lemmas to sum theorem 10
II. 2. Sum theorem 12
II.3. Decomposition theorem 16
II. 4. Product theorem 17
11.5. Strong inductive dimension and covering dimension ... 20
11.6. Some theorems characterizing dimension 25
II. 7. . The rank of a covering 28
II.8. Normal families 31
Chapter III. Mappings and dimension
111.1. Stable value 35
111.2. Extensions of mappings 37
111.3. Essential mappings 39
111.4. Some lemmas 43
III. 5. Continuous mappings which lower dimension 46
v
111.6. Continuous mappings which raise dimension 49
111.7. Baire s zero dimensional spaces 51
111.8. Uniformly zero dimensional mappings 55
Chapter IV. Dimension of separable metric spaces
IV. 1. Cantor manifolds 62
IV.2. Dimension of En 65
IV. 3. Some theorems in Euclidean space 68
IV.4. Imbedding 69
IV.5. e mappings 74
IV.6. Pontrjagin Schnlrelmann s theorem 76
IV. 7. Dimension and measure 81
IV.8. Dimension and the ring of continuous functions 86
Chapter V. Dimension and metrization 91
V.1. Characterization of dimension by a sequence of
coverings 93
V.2. Length of coverings 98
V.3. Dimension and metric function 102
V.4. Another metric that characterizes dimension 114
Chapter VI. Infinite dimensional spaces 123
VI. 1. Countable dimensional spaces 125
VI.2. Imbedding of countable dimensional spaces 132
VI. 3. Mappings and countable dimensional spaces 139
VI.4. Transfinite inductive dimension 141
VI.5. Sum theorem for transfinite inductive dimension . . . 148
VI.6. General imbedding theorem 154
Chapter VII. Dimension of non metrizable spaces
VII. 1. Sum theorem and subspace theorem for dim 158
VII. 2. Dimensions of non metrizable spaces 165
VII.3. Sum theorem and subspace theorem for Ind 170
VII.4. Characterization of dim by partitions 179
VII.5. Dimension and mappings 182
VII.b. Product theorem 192
VII. 7. Characterization by A, (X) 203
VII.8. Characterizations in terms of C(X) 2O7
Chapter VIII. Dimension and cohomology
VIII. 1. Homology group and cohomology group of a complex . . . .213
VIII.2. Cohomology group of a topological space 225
VIII.3. Dimension and cohomology 228
VIII.4. Dimension and homology 239
Bibliography 245
Additional Bibliography 258
List of Theorems 270
List of Definitions 273
Author index 275
Subject index 281
|
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 280 SK 290 |
| ctrlnum | (OCoLC)10085693 (DE-599)BVBBV000247614 |
| dewey-full | 513.83 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 513 - Arithmetic |
| dewey-raw | 513.83 |
| dewey-search | 513.83 |
| dewey-sort | 3513.83 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Rev. and extended ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:11:03Z |
| institution | BVB |
| isbn | 3885380021 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000149091 |
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| physical | IX, 284 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Heldermann |
| record_format | marc |
| series | Sigma series in pure mathematics |
| series2 | Sigma series in pure mathematics |
| spelling | Nagata, Jun-iti 1925-2007 Verfasser (DE-588)1052704034 aut Modern dimension theory J. Nagata Rev. and extended ed. Berlin Heldermann 1983 IX, 284 S. txt rdacontent n rdamedia nc rdacarrier Sigma series in pure mathematics 2 Topologie de l'espace métrique Distance geometry Dimensionstheorie (DE-588)4149935-9 gnd rswk-swf Dimensionstheorie (DE-588)4149935-9 s DE-604 Sigma series in pure mathematics 2 (DE-604)BV000012120 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000149091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nagata, Jun-iti 1925-2007 Modern dimension theory Sigma series in pure mathematics Topologie de l'espace métrique Distance geometry Dimensionstheorie (DE-588)4149935-9 gnd |
| subject_GND | (DE-588)4149935-9 |
| title | Modern dimension theory |
| title_auth | Modern dimension theory |
| title_exact_search | Modern dimension theory |
| title_full | Modern dimension theory J. Nagata |
| title_fullStr | Modern dimension theory J. Nagata |
| title_full_unstemmed | Modern dimension theory J. Nagata |
| title_short | Modern dimension theory |
| title_sort | modern dimension theory |
| topic | Topologie de l'espace métrique Distance geometry Dimensionstheorie (DE-588)4149935-9 gnd |
| topic_facet | Topologie de l'espace métrique Distance geometry Dimensionstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000149091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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