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Counterexamples in Topology
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.
272 pages, Paperback
First published January 1, 1970
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Displaying 1 - 9 of 9 reviews
May 5, 2017
A great companion to Munkres to have.
[Review 1 - 05/05/17.]
[Review 1 - 05/05/17.]
March 23, 2012
Topology is abstract enough that if you are learning the subject for the first time, and you are not constantly challenging yourself to come up with concrete applications and counterexamples, you will probably learn very little. If you find the requirements of a particular theorem to be a bit over-the-top and find yourself a few brain cells short of coming up with a proper counterexample to illuminate why the theorem is stated in that way, this book will be extremely useful. Even if you can always come up with one, some of these examples may be simpler or more illuminating. And at this price, there is no reason every mathematician should not have a copy.
July 8, 2009
Every student of topology should have this. Steen and Seebach provide instances to illustrate every distinction commonly made in topology (e.g. regular but not normal, T1 but not Hausdorff). In the latter part of the book the authors offer a thorough discussion of metrizability (under what conditions can a topological space be given a metric that "agrees" with its topology?).
July 23, 2020
This is a great side-piece to peruse during your topology studies. Read it alongside Munkres. It's just what it sounds like - a big list of examples. It can enrich your topology skills and deepen your understanding. Also, it's jam-packed with fascinating stuff.
June 9, 2019
Pretty perfect maths book. Does what it says on the tin. One thing I would recommend is that someone has built a database of topological spaces that includes most of these, so if you can't afford/your library doesn't have this book try this website:
June 27, 2008
I might have debated whether to give this 4 or 5 stars
if it had been a +$50 math book, but at $10, "the choice
(function) is clear ..."
if it had been a +$50 math book, but at $10, "the choice
(function) is clear ..."
March 17, 2009
As the title states, this book provides counterexamples in topology (that you were probably too lazy to come up with). Some of the examples were very critical in understanding topology at the undergraduate level, but as one may suspect, most of them were just so esoteric to the point of absurdity.
March 23, 2008
The Dover "Counterexamples in..." line is generally awesome; no exception here.
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January 27, 2019Topology
Displaying 1 - 9 of 9 reviews
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