Elementary Concepts of Topology (Dover Books on Mathematics) [Paperback]

Paul Alexandroff (Author)

Book Description

Publication Date: June 1, 1961 | Series: Dover Books on Mathematics

Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.

Product Details

• Paperback: 64 pages
• Publisher: Dover Publications; First edition. edition (June 1, 1961)
• Language: English
• ISBN-10: 048660747X
• ISBN-13: 978-0486607474
• Product Dimensions: 8.5 x 5.4 x 0.2 inches
• Shipping Weight: 3.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #861,816 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

5.0 out of 5 stars Excellent first exposure to algebraic topology., February 4, 2000

By 

Brent Smith (Redmond, WA) - See all my reviews
(REAL NAME)   

This review is from: Elementary Concepts of Topology (Dover Books on Mathematics) (Paperback)

This book is perfect for the advanced undergraduate--if you've taken modern algebra (groups, rings, fields, etc.), real analysis, some point-set topology, and are curious about algebraic topology, then this little book is time and money well spent. In about 50 relatively easy-to-read pages, you'll be able to sit down with your favorite topological spaces and actually do homological calculations. One of the book's main appeals is that it was originally published in 1932--well before homological algebra (aka "diagram chasing") obscured the beauty of algebraic topology.

8 of 8 people found the following review helpful:

5.0 out of 5 stars A Gem, February 23, 2001

By 

Colin McLarty (Chardon, OH USA) - See all my reviews

This review is from: Elementary Concepts of Topology (Dover Books on Mathematics) (Paperback)

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.

7 of 8 people found the following review helpful:

5.0 out of 5 stars a mental roadmap, June 1, 2001

By 

Ken Braithwaite (inkster, MI USA) - See all my reviews
(REAL NAME)   

This review is from: Elementary Concepts of Topology (Dover Books on Mathematics) (Paperback)

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).