Elementary Topology

Title page
Introduction
CHAPTER ONE: INTRODUCTORY SET THEORY
1. Introduction
2. Indexed Sets
3. The Theorem of DeMorgan
4. Cartesian Products. Introduction to Mappings
S. Relations, Mappings, Equivalence, Order
6. Sequences and Infinite Sets
7. Countab1e and Uncountable Sets
Bibliographical Comment
CHAPTER TWO: THE REAL LINE
1. Real Numbers and Sequences
2. Monotone Sequences
3. Cauchy Sequences
4. Open Sets
5. Connectcd Sets
6. Limit Points and Closed Sets
7. Closed and Bounded Sets
8. Continuous Functions
9. Properties of Continuous Functions
10. Summary
Bibliographical Comment
CHAPTER THREE: TOPOLOGICAL SPACES
1. Definitions and Examples
2. Metric Spaœs
3. Elementary Properties of Topological and Metric Spaces
4. Mappings and Subspaces
5. Connected Sets
Bibliographical Comment
CHAPTER FOUR: METRIC SPACES
1. Elementary Properties of Metrics and Metric Spaces
2. Local Connectivity and the introduction of an M Metric
3. Sequences
4. Second Countable Spaces
S. Metrizability
6. The metrization of Regular, Second Countable T1 Space
7. Extension of Mappings
8. Function Spaces
9. The Completion of Metric Spaces
10. The Euclidean Spaces
Rihliographical Comment
CHAPTER FIVE: ARCS AND CURVES
1. The Arc and Naturally Ordered Collections of Sets
2. The Arc
3. Simple Closed Curves
4. The Jordan Curve Theorem
S. Peano Spaces
6. Property S
7. The Cyc1ic Connectivity Theorem
8. Local Compactness and the Relationship between E² and the Sphere
9. Simple Closed Surfaces
Ribliographical Comment
CHAPTER SIX: PARTITIONABLE SPACES
1. Introduction to Partitionability
2. The Equivalence of Partitionability and Property S
Ribliographical Comment
CHAPTER SEVEN: THE AXIOM OF CHOICE
1. Partial, Simple, and Well-Orderings
2. Alternative Forms of the Axiom of Choice
3. Examples of Applications of the Axiom of Choice
Bibliographical Comment
LIST OF SPECIAL SYMBOLS
INDEX