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Type of bind: Paperback
Dewey Decimal Number: 514
EAN num: 9780486663524
ISBN number: 0486663523
Label: Dover Publications
Manufacturer: Dover Publications
Quantity: 1
Page Count: 224
Printing Date: July 01, 1990
Publishing house: Dover Publications
Sale Popularity Level: 92731
Studio: Dover Publications
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Editor's Notes and Comments:
Product Description:
An undergraduate introduction to the fundamentals of topology — engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject.
User popularity level:
Rated by buyers -
This is a terrific introduction to topology. The problems are especially well chosen -- working through the problems will maximize your understanding. Competance in undergrad calculus is probably all that you'll need. Well written -- I can't imagine another book on the subject that would be more approachable.
Rated by buyers -
This is a great introduction to topology for undergraduates! I highly recommend it's use as a text since there are no solutiions in the back. The minute I got my hands on it, I fell in love. However, this book may need to be supplemented by other material in a topology class.
Rated by buyers -
This is a wonderful book to start your topological studies with. It has many problems for one to do so one can practice and study and have the ability to make the grade on one's tests
Rated by buyers -
I bought this book for my own enlightenment after already having a course in Topology here at Penn State University. What I find most interesting about this book is that the author explains the philosophy on the ideas and what we are really trying to say with these definitions and theorems. The book I used in my course didn't explain much at all so it would have been much more difficult to teach yourself from this book. Topology is somewhat abstract so if you're looking to study Topology this is a great book to start. A word of advice, read over a theorem and proof and try to reproduce it on paper from your mind. Help yourself from the book a bit along the way if necessary. You will learn much more this way as opposed to following along the proofs in the book as you read. You might also be interested in Counterexamples in Topology, a book with thousands of counterexamples.
Rated by buyers 
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I was not a mathematics major, and only in recent years have I ventured into abstract mathematics. I was motivated to learn about topology as an aid to understanding a particular 3-D earth modeling application.
I read Introduction to Topology in three stages: as a review of set theory and metric spaces (chapters 1 and 2), then as an introduction to topology (chapter 3), and lastly as a detailed look at two important topological properties, connectedness (chapter 4) and compactness (chapter 5). I had previously read (and reviewed) another book titled Metric Spaces by Victor Bryant, but Mendelson is my very first serious look at topology.
My reading of Mendelson - a 200-page text - required about 100 hours, substantially longer than the 40 to 60 hours estimated by an earlier reviewer. No solutions are provided for the section problems, which are generally proofs, not explicit problems.
The very first chapter provides a concise overview of set theory and functions that is essential for Mendelson's later chapters on subsequent set-theoretic analysis of metric spaces and topology.
The second chapter is a solid introduction to metric spaces with good discussions on continuity, open balls and neighborhoods, limits from a metric space perspective, open sets and closed sets, subspaces, and equivalence of metric spaces. Chapter 2 concludes with a brief introduction to Hilbert space.
The third chapter introduces topological spaces as a generalization of metric spaces, and many theorems are largely restatements of the metric space theorems derived in chapter 2. I was thankful for this approach.
Mendelson begins chapter 3 by demonstrating that 1) open sets and neighborhoods are preserved in passing from a metric space to its associated topological space and 2) the existence of a one to one correspondence between the collection of all topological spaces and the collection of all neighborhood spaces.
He then reminds us that in a metric space we can say that there are points of a subset A arbitrarily close to a point x if the metric d(x, A) = 0. In characterizing this notion of arbitrary closeness in a topological space, Mendelson introduces the closure of A, the interior of A, and the boundary of A. Other topics included topological functions, continuity, homeomorphism (the equivalence relation), subspaces, and relative topology. The final sections in chapter 3 on products of topological spaces, identification topologies, and categories and functors were more difficult.
In chapter 4 the initial sections (connectedness on the real line, the intermediate value theorem, and fixed point theorems) were largely familiar. But thereafter I became bogged down with the discussions of path-connected topological spaces, especially with the longer proofs involving the concepts of homotopic paths, the fundamental group, and simple connectedness.
Chapter 5, titled Compactness, was even more abstract and difficult, with topics like coverings, finite coverings, subcoverings, compactness, compactness on the real line, products of compact spaces, compact metric spaces, the Lebesgue number, the Bolzano-Weierstrass property, and countability. Perhaps, a reader more familiar with analysis would have less difficulty with the last two chapters.
In summary, Introduction to Topology is quite useful for self-study. Mendelson's short text was intended for a one-semester undergraduate course, and it is thereby ideal for readers that either require a basic introduction to topology, or need a quick review of material previously studied. The last two chapters on connectedness and compactness are substantially more difficult, but are still accessible to the persistent reader.
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