Shape Theory

The Inverse System Approach

S. Mardešic, J. Segal

• Publisher: North Holland
• Year: 1982
• ISBN:
  9780080960142
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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.

Table of contents

• Front Cover
• Shape Theory: The Inverse System Approach
• Copyright Page
• Table of Contents
• Dedication
• PREFACE
• INTRODUCTION
• CHAPTER I. FOUNDATIONS OF SHAPE THEORY
• CHAPTER II. SHAPE INVARIANTS
• CHAPTER III. A SURVEY OF SELECTED TOPICS
• APPENDICES
• BIBLIOGRAPHY
• LIST OF SPECIAL SYMBOLS
• SUBJECT INDEX