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Counterexamples in Analysis

4.03  ·  Rating details ·  73 ratings  ·  7 reviews
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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Min
Mar 22, 2019 rated it really liked it
Shelves: math
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
Scott
May 16, 2008 rated it did not like it
Shelves: textbooks
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
Dec 26, 2011 rated it liked it
Recommends it for: Mathematics majors
Shelves: analysis
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
Aug 30, 2012 rated it really liked it
Shelves: technical, math
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 ....
Stephen
Mar 17, 2009 rated it liked it
Shelves: mathematics
The book contains some important examples, but most of them are too arcane and inelegant.
Nick Black
Mar 23, 2008 rated it really liked it
Not as absolutely outstanding as "Counterexamples in Topology", but necessary reading to be sure.
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