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Title: Elementary Concepts of Topology by Paul Alexandroff ISBN: 0-486-60747-X Publisher: Dover Pubns Pub. Date: 01 June, 1961 Format: Paperback Volumes: 1 List Price(USD): $5.95 |
Average Customer Rating: 4 (4 reviews)
Rating: 1
Summary: A very bad topology book
Comment: When a book is translated it is supposed to be in English... this book is in topology as a language of it's own. For me with a library and long history of reading topology books, it is understandable. The author is recognized as a great mathematician, but I think he should have had his maiden aunt read his proofs for the book... he writes badly of topology and his references aren't anywhere near clear enough. I suppose it is that I found that his treatment of the tetrahedron and projective plane really don't work well when translated to numbers....
Rating: 5
Summary: a mental roadmap
Comment: A very slender book, but it sets out the basic ideas of algebraic topology and HOW THEY RELATE TO EACH OTHER. A roadmap to what all this simplex stuff is all about.
For sophisticated mathematical readers only. Perfect adjunct to any first course.
(And a "lemniscate" is a figure 8).
Rating: 5
Summary: A Gem
Comment: A great book, born in a great moment of mathematics. Alexandroff explains, and shows in pictures, what topology is basically about and why "homology groups" are the way to do it.
Anyone can follow this who has had multivariable calculus, plus seen the definition of a group (as in, say, arithmetic modulo 2). In 55 profusely illustrated yet rigorous pages Alexandroff shows how to define topological manifolds, cut them into "simplices", and keep track of simplices algebraically. He proves the two founding theorems of topology: the dimension of manifolds, and their homology groups, are both preserved by topological isomorphisms.
Alexandroff was a favorite student of Emmy Noether, and L.E.J. Brouwer, and followed Hilbert's lectures. The greatest algebraist, the greatest topologist, and the greatest mathematician of the early 20th century all had direct input into this book. All believed the most important, deepest mathematics can be made the clearest. They were right.
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Title: Introduction to Topology : Third Edition by Bert Mendelson ISBN: 0486663523 Publisher: Dover Pubns Pub. Date: 01 July, 1990 List Price(USD): $10.95 |
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Title: Introduction to Topology : Second Edition by Theodore W. Gamelin, Robert Everist Greene ISBN: 0486406806 Publisher: Dover Pubns Pub. Date: 16 June, 1999 List Price(USD): $12.95 |
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Title: Topology by John G. Hocking, Gail S. Young ISBN: 0486656764 Publisher: Dover Pubns Pub. Date: 01 June, 1988 List Price(USD): $14.95 |
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Title: Algebraic Topology by C. R. F. Maunder ISBN: 0486691314 Publisher: Dover Pubns Pub. Date: 14 June, 1996 List Price(USD): $16.95 |
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Title: Experiments in Topology by Stephen Barr ISBN: 0486259331 Publisher: Dover Pubns Pub. Date: 01 March, 1989 List Price(USD): $9.95 |
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