书名：Counterexamples in Analysis数学分析中的反例

作者：B. R. Gelbaum;J. M. H. Olmsted 

出版社名称：Dover Publications Inc. 

出版时间：2003

语种：英语 

ISBN：9780486428758 

商品尺寸：16.2 x 1.2 x 21.5 cm

包装：平装

页数：218（以实物为准）

这些根据难度或复杂程度排列的反例主要处理从演算级别开始的分析部分，即“实际变量”。本书的前半部分介绍了实变量的功能。主题包括实数系统，函数和极限，微分，Riemann积分，序列，无穷级数，一致收敛以及实轴上的集合和度量。下半部分涵盖了更高的维度，研究了两个变量的功能，即平面集，面积，度量和拓扑空间以及函数空间。该卷包含许多内容，将证明它们适合尚未完成微积分第一门课程的学生，并且对于高级分析学生和研究生也有足够的兴趣。

These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as "real variables," starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, encompassing higher dimensions, examines functions of two variables, plane sets, area, metric and topological spaces, and function spaces. This volume contains much that will prove suitable for students who have not yet completed a first course in calculus, and ample material of interest to more advanced students of analysis as well as graduate students. 12 figures. Bibliography. Index. Errata.

1. The Real Number System.

2. Functions and Limits.

3. Differentiation.

4. Riemann Integration.

5. Sequences.

6. Infinite Series.

7. Uniform Convergence.

8. Sets and Measure on the Real Axis.

9. Functions of Two Variables.

10. Plane Sets.

11. Area.

12. Metric and Topological Spaces.

13. Function Spaces.

Bibliography. Special Symbols. Index.