A Primer of Real FunctionsPDF电子书下载

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