Counterexamples in Analysis

by Bernard R. Gelbaum, John M. H. Olmsted

These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.

Genres: Mathematics, Textbooks, Nonfiction, Reference, Science

224 pages, Paperback

First published June 4, 2003

Reviews

[Tomáš Ševček]

With all the problems of this book mentioned in the other comments, I highly recommend this book (as a complementary reading to a standard analysis text like Baby Rudin) to anyone who wants to understand analysis well. Sometimes, one might think that they understand a certain concept until they encounter a counterexample to something they considered true. And this book contains a plenty of counterexamples - from the very basics of analysis up to the measure theory and metric and topological spaces. Do not expect to find counterexamples from complex analysis though - it is much "better-behaved" than real analysis, so there are not as many counterexamples to be found at the introductory level.

[Scott]

The book itself was not horribly written or otherwise deplorable, but the fonts and symbols chosen to represent various characters in mathematics were very atypical and made for an often-confusing read. Other books do a much better job of delineating the same material in a more consistent and transparent manner.

[Ronald Lett]

Although it does give some rather arcane examples where a detailed abstract description would have sufficed, it does give a concise collection of concrete counterexamples, some of which may have slipped under your radar.

[Ray]

A good book for students of analysis - it presents thoughtful counterexamples, illustrating why certain theorems are phrased the way they are. Also useful for those occasions when you need to construct functions, or sequences of functions, with relatively bizarre properties ....

[Nick Black]

Not as absolutely outstanding as "Counterexamples in Topology", but necessary reading to be sure.

[Stephen]

The book contains some important examples, but most of them are too arcane and inelegant.

[Goo]

En fin bog til at indse hvad der ikke gælder.

[Dennis]

http://pro-libertate.net/20140325/234...