Shape Theory: An Introduction

Chapter I. Introduction
Chapter II. Preliminaries
§1. Topology
§2. Homotopy Theory
§3. Category Theory
CHAPTER III. THE SHAPE CATEGORY
§1. Definition of the Shape Category
§2. Some properties of shape category and shape functor
§3. Representation of shape morphisms
§4. Borsuk's approach to shape theory
§5. Chapman' s Complement Theorem
Chapter IV. General Properties of the Shape Category and the Shape Functor
§1. Continuity
§2. Inverse Limits in the Shape Category
§3. Fox's Theorem in Shape Theory
§4. Shape Properties of Some Decomposition Spaces
§5. Space of Components
Chapter V. Shape Invariants
§i. Čech homology, cohomology and homotopy pro-groups
§2. Movability and n-movability
§3. Deformation Dimension
Chapter VI. Algebraic Properties Associated with Shape Theory
§1. The Mittag-Leffler condition and the use of lim¹
§2. Homotopy idempotents
Chapter VII. Pointed 1-movability
§1. Definition of pointed 1-movable continua and their properties
§2. Representation of pointed 1-movable continua
§3. Pointed 1-movability on curves
Chapter VIII. Whitehead and Hurewicz Theorems in Shape Theory
§1. Preliminary results
§2. The Whitehead Theorem in shape theory
§3. The Hurwicz Theorem in shape theory
Chapter IX. Characterizations and Properties of Pointed ANSR's
§1. Preliminary results
§2. Characterizations of pointed ANSR's
§3. The Union Theorem for ANSR's
§4. ANR-divisors
Chapter X. Cell-like Maps
§1. Preliminary definitions and results
§2. The Smale Theorem in shape theory
§3. Examples of cell-like maps which are not shape equivalences
§4. Hereditary shape equivalences
Chapter XI. Some Open Problems
Bibliography
Dydak, J., and A. Kadlof
Karras, A., W. Magnus, and D. Solitar
McMillan, D.R., Jr.
Watanabe, T.
List of Symbols
Index