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General Topology (Dover Books on Mathematics) [Paperback]

by Stephen Willard
4.6 out of 5 stars  See all reviews (15 customer reviews)

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Book Description

February 27, 2004 0486434796 978-0486434797
Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Its treatment encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by nine sections on connectivity properties, topological characterization theorems, and homotopy theory. Many standard spaces are introduced in the related problems that accompany each section (340 exercises in all). The text's value as a reference work is enhanced by a collection of historical notes, a bibliography, and index. 1970 edition. 27 figures.

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General Topology (Dover Books on Mathematics) + Introduction to Topology: Third Edition (Dover Books on Mathematics)
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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 384 pages
  • Publisher: Dover Publications (February 27, 2004)
  • Language: English
  • ISBN-10: 0486434796
  • ISBN-13: 978-0486434797
  • Product Dimensions: 2.4 x 3.7 x 0.3 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #534,629 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews
39 of 40 people found the following review helpful
One of the purest and most intellectually challenging branches of modern mathematics, general topology is not a subject for the faint hearted. So it was a pleasure when I first encountered one of the best reference introductions to the subject to have seen the light of day. Willard's book remains one of my all-time favourites. It covers everything the aspiring topologist needs to know, and certainly supplies more than enough information for a potential PhD student to choose their initial area of specialisation. The chapters are split intelligently into sub-topics which move at a sensible pace from its introductory notes on essential set theory, through subspaces, products, compactness, separation and countability axioms, compactifications, and function spaces. Many of the "standard spaces" of general topology are introduced and examined in the large number of related problems accompanying each section. And for those wanting a bit more context than a maths book normally provides there's a detailed collection of historical notes for each chapter.
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19 of 19 people found the following review helpful
5.0 out of 5 stars A masterpiece February 14, 2008
First a caveate: This book may not be the most suitable for everyone that takes a FIRST course on General Topology unless he or she is prepared to put in quite a lot of work. This is because the book contains so much information in relatively few pages that the material is necessarily quite dense. Even so the book is a good purchase because it's cheap and will serve everyone good later as a reference.

The organization of the book: Everything is presented in a perfectly logical order, beginning with a summary of Set Theory and ending with topologies on Function Spaces. During the course the reader is invited to make excursions to other areas of mathematics from a topological point of view and perhaps gain insights into those fields that even specialists don't have. This is mostly done through problems for the reader to solve.

Definitions and Theorems: The definitions are always the most general possible, often presented as a set of axioms that the defined quantity has to fulfill. The theorems are almost always presented in their most general form.

The Proofs: The proofs are generally on either the shortest and most elegant form possible, or taken from the original publications. This is for the benefit of the reader even though it might appear to some readers as "terse" proofs because this kind of proofs is the one that gains the reader the most insight once they are understood. "Short and elegant" does NOT mean that the author leaves out details (unless they are explicitely assigned as problems).

Explanations and Motivations: The text is short and to the point. This again does not mean that the author leaves out anything relevant or that he does not warn for possible pitfalls.
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17 of 19 people found the following review helpful
5.0 out of 5 stars goldmine of information; this is hidden treasure July 28, 2005
I have yet to see Dugundji's topology text (it's always checked out at my university library) but I would still guess that this is one of the best there is. Willard's book most certainly covers all the topics that "every young analyst should know", as Kelley wrote, but I think this book outdoes Kelley's when it comes to that! It covers topics like convergence, separation & countability, compactness, connectedness, uniform spaces & a short discussion on function spaces & C* algebras at the end. Many of the theorems, proofs & examples come directly from the original source articles, or are the most general versions there is. Each section has a very detailed & interesting historical discussion at the end of the book where the author lists the original articles & the circumstances in which they were published & other stuff. Where the text really stands out though is the problem sets. As the reader goes deeper into the book of course the concepts get more complicated & proofs of extremely deep & important results are outlined as problems. These are things such as the Cantor-Bernstein theorem, Hahn-Banach theorem, Pontryagin duality theorem, stuff about realcompactness, Edwin Hewitt's construction of a regular T1 space in which every continuous function is constant(!) & many more. Don't be afraid though; the discussion in the text, hints given & notes in the back help with proving things like those. Many of the examples are also highly nontrivial & therefore very helpful (imho). To sum up, I believe this book is very underrated & deserves the recognition of the texts by Munkres & Kelley.
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10 of 11 people found the following review helpful
5.0 out of 5 stars Wilard's Topology March 10, 2006
After looking at several books on topology, I would have to say that Wilard's General Topology is an excellent resource book. For those who have taken a topology course and want a little more practice with problems, this book has numerious exercises that help form an solid knowledge base. What else is nice about the problems is they are good research-starters for undergraduates. The examples in the chapters are non-trivial and explain the ideas of the chapter. Also, Wilard's General Topology has a slight set-theoritic view to topology, so those who like set-theory and topology, this book will be of great use. I suggest Wilard's General Topology if you need another topology book to help explain ideas from class or other books.
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Most Recent Customer Reviews
5.0 out of 5 stars I love the book.
I am greatly impressed; as the book is what I have been looking for. I recommend it for every student in Maths class.
Published 10 months ago by Asogwa Sunday A
5.0 out of 5 stars Excellent is was I expected in this product.
Excellent is was I expected in this product for my niece. She needed for study in the university. Ok, !!!!!
Published 13 months ago by JL
4.0 out of 5 stars A Lot of Stuff
Great book with a lot of good stuff, especially in the exercises. However, if you're not willing to work through the relatively dense exercises, you might want to look for... Read more
Published on April 2, 2011 by math4tots
5.0 out of 5 stars The best general topology book.
I'll write this rate for those who doesn't know ANYTHING about topology, as it was my case before meeting this book. Read more
Published on February 21, 2011 by Daniel
5.0 out of 5 stars Great book but a few errors.
I taught myself from this book my senior year in high school and I absolutely loved it.


The cost is amazing. Read more
Published on January 17, 2011 by Reid H
3.0 out of 5 stars agonizing to use as a reference
The back cover blurb describes this book as "among the best available reference introductions to general topology." Notice that word "reference. Read more
Published on October 14, 2010 by Benjamin Crowell
5.0 out of 5 stars Absolutely amazing!
This is certainly one of the best books on general topology available. It requires more maturity from the reader than the usual Munkres/Armstrong standard, but IMHO it is perfectly... Read more
Published on January 23, 2010 by Rodrigo Barbosa
5.0 out of 5 stars A Great Beginning Text
Willard's text is a great introduction to the subject, suitable for use in a graduate course. I am personally not training to be a topologist but I must say that I enjoyed this... Read more
Published on June 18, 2008 by ikantspel
5.0 out of 5 stars Excellent
this is an amazing book. very wisely constructed with a lot of real content.
if i may ask for something more i would ask for an updated version, and solutions for problems.
Published on December 7, 2007 by Amazon Customer
5.0 out of 5 stars Topology encyclopedia
Every mathematician needs this book if she/he wants to learn topology. You can use it to learn and as a reference. Furthermore, this book has an extensive bibliography.
Published on February 8, 2007 by Gabriel Girón-Garnica
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