**Book Title:** Counterexamples in Analysis (Dover Books on Mathematics)

**Publisher:** Dover Publications

**ISBN:** 0486428753

**Author:** Bernard R. Gelbaum

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**Book Title:** Counterexamples in Analysis (Dover Books on Mathematics)

**Publisher:** Dover Publications

**ISBN:** 0486428753

**Author:** Bernard R. Gelbaum

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- Counterexamples in Topology (Dover Books on Mathematics)
- Counterexamples in Probability: Third Edition (Dover Books on Mathematics)
- Principles of Mathematical Analysis
- Topology
- Elements of the Theory of Functions and Functional Analysis [Two Volumes in One]
- How to Think About Analysis
- Introduction to Topology: Third Edition (Dover Books on Mathematics)
- A Book of Abstract Algebra: Second Edition (Dover Books on Mathematics)
- Abstract Algebra
- Real & Complex Analysis

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.