CHAPTER 1．SETS 1
1．Sets 1
2．Sets of real numbers 4
3．Countable and uncountable sets 7
4．Metric spaces 18
5．Open and closed sets 22
6．Dense and nowhere dense sets 32
7．Compactness 38
8．Convergence and completeness 44
9．Nested sets and Baire＇s theorem 53
10．Some applications of Baire＇s theorem 57
11．Sets of measure zero 62
CHAPTER 2．FUNCTIONS 65
12．Functions 65
13．Continuous functions 70
14．Properties of continuous functions 75
15．Upper and lower limits 83
16．Sequences of functions 85
17．Uniform convergence 88
18．Pointwise limits of continuous functions 99
19．Approximations to continuous functions 102
20．Linear functions 108
21．Derivatives 113
22．Monotonic functions 128
23．Convex functions 142
24．Infinitely differentiable functions 150
NOTES 157
ANSWERS TO EXERCISES 163
INDEX 181