Lecture Notes Topology (2301631) Phichet Chaoha Department of ...

Contents
Preliminaries 5
Sets and Maps 5
Countable and Uncountable Sets 5
Ordered Sets 6
Chapter 1. Basic Concepts in Topology 7
1. Spaces and Subspaces 7
2. Basis for a Topology 11
3. Limit Points 14
4. Continuous Maps 17
5. Sequences and Nets 21
6. Product Topology 23
7. Quotient Topology 26
8. Metric Topology 29
Chapter 2. Countability and Separation Axioms 33
1. The Countability Axioms 33
2. The Separation Axioms 35
Chapter 3. Connectedness 41
Chapter 4. Compactness 47
Chapter 5. Function Spaces 59
Chapter 6. Complete Metric Spaces 65
Bibliography 73
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