CHAPTER 0 PRELIMINARIES
1. Introduction
2. Sets
3. The Algebra of Sets
4. Euler-Venn Diagrams
5. Relations
6. Infinite Sets
7. Miscellaneous Assumptions Regarding the Real Numbers
CHAPTER 1 TOPOLOGICAL SPACES-BASIC DEFINITIONS AND THEOREMS
1. Neighborhood Systems and Topologies
2. Open Sets in a Topological Space
3. Limit Points and the Derived Set
4. The Closure of a Set
5. Closed Sets
6. Subspaces
7. Limits of Sequences; Hausdorff Spaces
8. Comparison of Topologies
9. "Bases, Countability Axions, Separability"
10. "Sub-bases, Product Spaces"
CHAPTER 2 CONTINUOUS FUNCTIONS (MAPPINGS) AND HOMEOMORPHISMS
1. Functions
2. Continuous Functions (Mappings)
3. Homeomorphisms
4. Product Spaces
CHAPTER 3 VARIOUS SPECIAL TYPES OF TOPOLOGICAL SPACES (VARIETIES OF COMPACTNESS)
1. Compact Spaces
2. Separation Axioms
3. Countable Compactness
4. Local Compactness
CHAPTER 4 FURTHER SPECIAL TYPES OF TOPOLOGICAL SPACES (MOSTLY VARIETIES OF CONNECTEDNESS)
1. Introduction
2. Connected Spaces
3. Components
4. Local Connectedness
5. Arcwise Connectedness
CHAPTER 5 METRIC SPACES
1. Definitions
2. Some Properties of Metric Spaces
3. Metrization Theorems
4. Complete Metric Spaces
5. Category Theorems
REFERENCES
INDEX