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Counterexamples in Analysis
These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the bookdiscusses 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. ...more
Paperback, 224 pages
Published June 4th 2003 by Dover Publications
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I probably would have given this book a lower rating if not for some of the reviews on this site. First, there are plenty of problems with this book. Much of the preliminary material is written in a compact manner that is difficult to understand for those not already familiar with the subject. Many details are left out with references to fill in the blanks; this is excluding the use of major theorems. It is not always clear what the counterexamples are counterexamples of. There is virtually no ...more
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.
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.
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 ....
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