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Synopsis
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 construct
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Most Helpful Customer Reviews
16 of 16 people found the following review helpful:
4.0 out of 5 stars
-- -- A counterexample to the standard topology book -- --,
By A Customer
This review is from: Counterexamples in Topology (Dover Books on Mathematics) (Paperback)
This is not your typical topology text. In the first part of the book, the authors give a crash course on basic point-set topology. Rather than proving theorems, the emphasis is on defining and explaining concepts, especially as the various concepts relate to each other. The explanations are not always sufficient in themselves for the student's understanding, but that wasn't the book's mission. In the second part, the book provides "Counterexamples": quite a few topologies, both the predictable and the quirky kinds. The topologies given vary considerably in level of difficulty. Thirdly, several pages at the end provide charts showing which properties the book's listed topologies have. The reader can use these charts to find a suitable topology for many applications or disproofs. Counterexamples in Topology is both useful and enjoyable, particularly for people who benefit from charts and outlines. It is not a book to be plowed through, page by page, like a textbook. Rather, it is a compendium of several interesting cases, any of which can be studied independently of the rest.
1 of 1 people found the following review helpful:
5.0 out of 5 stars
All praise to Dover,
This review is from: Counterexamples in Topology (Dover Books on Mathematics) (Paperback)
Steen and Seebach's book, first published forty years ago, is a cornucopia of examples. You want a separable first countable completely regular space which is not normal, and which has an uncountable discrete subspace? Niemytzki's tangent disc topology fills the bill. Thanks to Dover, this beautifully printed and bound reprint comes at a ridiculously low price: buy it!
5.0 out of 5 stars
Not a textbook, but a great survey,
By Garrold (London) - See all my reviews
This review is from: Counterexamples in Topology (Dover Books on Mathematics) (Paperback)
This book is a classic. I bought this book because I was trying to understand the range of topologies that exist, which this book achieves. It also systematically classifies topologies by their topological properties, and summarised the information in tables at the back of the book. This book is a not a text book, but I learnt a lot by browsing it.
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