Shape Theory (eBook)

The Inverse System Approach

S. Mardesic, J. Segal (Autoren)

eBook Download: PDF

1982 | 1. Auflage
393 Seiten
Elsevier Science (Verlag)
978-0-08-096014-2 (ISBN)

Infos

North-Holland Mathematical Library, Volume 26: Shape Theory: The Inverse System Approach presents a systematic introduction to shape theory by providing background materials, motivation, and examples, including shape theory and invariants, pro-groups, shape fibrations, and metric compacta. The publication first ponders on the foundations of shape theory and shape invariants. Discussions focus on the stability and movability of spaces, homotopy and homology pro-groups, shape dimension, inverse limits and shape of compacta, topological shape, and absolute neighborhood retracts. The text then takes a look at a survey of selected topics, including basic topological constructions and shape, shape dimension of metric compacta, complement theorems of shape theory, shape fibrations, and cell-like maps. The text ponders on polyhedra and Borsuk's approach to shape. Topics include shape category of metric compacta and metric pairs, homotopy type of polyhedra, and topology of simplicial complexes. The publication is a valuable source of data for researchers interested in the inverse system approach.

Inhalt

Front Cover 1
Shape Theory: The Inverse System Approach 4
Copyright Page 5
Table of Contents 10
Dedication 6
PREFACE 8
INTRODUCTION 14
CHAPTER I. FOUNDATIONS OF SHAPE THEORY 18
§1. PRO-CATEGORIES 20
§2. ABSTRACT SHAPE 35
§3. ABSOLUTE NEIGHBORHOOD RETRACTS 50
§4. TOPOLOGICAL SHAPE 62
§5. INVERSE LIMITS AND SHAPE OF COMPACTA 71
§6. RESOLUTIONS OF SPACES AND SHAPE 90
CHAPTER II. SHAPE INVARIANTS 110
§1. SHAPE DIMENSION 112
§2. PRO-GROUPS 123
§3. HOMOTOPY AND HOMOLOGY PRO-GROUPS 137
§4. HUREWICZ THEOREM IN SHAPE THEORY 151
§5. WHITEHEAD THEOREM IN SHAPE THEORY 160
§6. MOVABILITY OF PRO-GROUPS 175
§7. MOVABILITY OF SPACES 195
§8. n- MOVABILITY OF SPACES 215
§9. STABILITY OF SPACES 235
CHAPTER III. A SURVEY OF SELECTED TOPICS 258
§1. BASIC TOPOLOGICAL CONSTRUCTIONS AND SHAPE 261
§2. SHAPE DIMENSION OF METRIC COMPACTA 267
§3. SHAPE OF COMPACT CONNECTED ABELIAN GROUPS 270
§4. SHAPE OF THE STONE-CECH COMPACTIFICATION 273
§5. LCn DIVISORS AND CONTINUA WITH LCn SHAPE 276
§6. COMPLEMENT THEOREMS OF SHAPE THEORY 279
§7. EMBEDDINGS UP TO SHAPE 285
§8. SHAPE FIBRATIONS 287
§9. STRONG SHAPE 294
§10. CELL-LIKE MAPS 300
APPENDICES 304
APPENDIX 1: POLYHEDRA 306
§1. TOPOLOGY OF SIMPLICIAL COMPLEXES 306
§2. THE HOMOTOPY TYPE OF POLYHEDRA 327
§3. THE CECH EXPANSION 341
APPENDIX 2. BORSUK'S APPROACH TO SHAPE 346
§1. SHAPE CATEGORY OF METRIC COMPACTA 346
§2. SHAPE CATEGORY OF COMPACT METRIC PAIRS 353
BIBLIOGRAPHY 358
LIST OF SPECIAL SYMBOLS 389
SUBJECT INDEX 392

Produkt-Details

• Erscheint lt. Verlag: 1.1.1982
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 0-08-096014-6 / 0080960146
• ISBN-13: 978-0-08-096014-2 / 9780080960142