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Introduction to Topology: Third Edition (Dover Books on Mathematics) Third Edition

by Bert Mendelson (Author)
4.5 out of 5 stars 452
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Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.
Previous page
  1. ISBN-10
    0486663523
  2. ISBN-13
    978-0486663524
  3. Edition
    Third
  4. Publisher
    Dover Publications
  5. Publication date
    July 1, 1990
  6. Part of series
    Dover Books on Mathematics
  7. Language
    English
  8. Dimensions
    5.44 x 0.45 x 8.41 inches
  9. Print length
    224 pages
  10. See all details
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Introduction To Topology (0486663523)

Ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.

Editorial Reviews

From the Back Cover

Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. The book's principal aim is to provide a simple, thorough survey of elementary topics in the study of collections of objects, or sets, that possess a mathematical structure.The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. In the second chapter Professor Mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness. Throughout the text, Dr. Mendelson, a former Professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.
Unabridged Dover (1990) republication of the edition published by Allyn and Bacon, Inc., Boston 1975.

Product details

  • Publisher ‏ : ‎ Dover Publications; Third edition (July 1, 1990)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 224 pages
  • ISBN-10 ‏ : ‎ 0486663523
  • ISBN-13 ‏ : ‎ 978-0486663524
  • Item Weight ‏ : ‎ 9.9 ounces
  • Dimensions ‏ : ‎ 5.44 x 0.45 x 8.41 inches
  • Customer Reviews:
    4.5 out of 5 stars 452

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Bert Mendelson

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Customer reviews

4.5 out of 5 stars
4.5 out of 5
452 global ratings

Top reviews from the United States

DOC
5.0 out of 5 stars Good introductory level book
Reviewed in the United States on February 11, 2018
Verified Purchase
This is an entry level book about general topology (or point set topology). The book is written in a clear and well-organized manner, quite easy to follow. It's worth mentioning that aside from the rigorous statement of concepts/theorems, the author also made an effort to explain how and why people get there. This helps me gain the mathematical intuition about the topics, and hence gain better and structured understanding and make the topics really a solid part of my knowledge. The problems are quite gentle and proper for beginners. BTW, I am not majored in mathematics, but I feel quite comfortable going through this book. Quite pleasant reading experience.
14 people found this helpful
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W. L. Ohm
5.0 out of 5 stars Introduction to topology
Reviewed in the United States on March 20, 2019
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The book is a very basic book on topology. It is very readable. You do not need to be a "great" mathematician to read this book. The references are good too. But, the reference are older books. I have read some of his references. I will use the book to help a person learn topology. It will get him started. Also, each chapter has one main topic, which is very
nice. And, another good thing about the book is that it has a reasonable amount of pages.
5 people found this helpful
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Guillermo Angeris
5.0 out of 5 stars Great introduction, especially for self-study
Reviewed in the United States on December 18, 2015
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Overall, great introductory book to topology. The pedagogy was excellent and the development of topics <i>made sense</i> in going from metric spaces (a notion that is general more intuitive) to abstract topological spaces.

In particular, it was great for self-study as Mendelson doesn't shy away from fully fleshing-out proofs and repeating relatively similar cases with some additional notes (e.g. when going from metric to topological spaces and proving several ideas there). The book itself can certainly be read by anyone with a set theory background and some intuitive notion of limits/sequences (i.e. a class in pre-calculus), but that doesn't mean it's easy, <i>by any means</i>. I struggled quite a bit with the intuition behind some of the proofs, and have, more than once, rolled around on my bed trying to recall (or prove again) some particular statement that I found quite useful. Sadly, the book doesn't have a section on homotopy equivalence and some other useful notions, but do recall it is an introduction in exactly 200 pages of short text.

This book took me at least 20-30 hours to get through, skipping only the very latter section on compactess and doing at least two of the harder problems in each section; but I have very little experience with analysis, something I'm sure would have helped complete this and gain the corresponding intuition much more quickly.

Again, great book and would highly recommend it for self-study of topology.
41 people found this helpful
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FiziksGangsta
4.0 out of 5 stars Great for the price
Reviewed in the United States on January 24, 2012
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I had one semester of real analysis prior to picking up this book. I found it's presentation of metric spaces OK, though Mendelson seems happy enough with abstract definitions that he doesn't always try to help with developing some intuition. This book is probably pretty hard to read if you're not familiar with metric spaces.

Mendelson introduces topological spaces very well, though, with lots of examples, counterexamples, and explanations of both. It's dense reading (though not open-dense, ha-ha) but it is worth it. Definitely a good first book on topology.
One person found this helpful
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PC_Customer
5.0 out of 5 stars A great book for those non-mathematicians who need to fill the gaps!
Reviewed in the United States on June 28, 2019
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After working in industry, I started grad school in control theory. As expected, I realized that I needed to fill a lot of basic concepts on point-set topology to further understand many of the proofs found in prestigious conferences and journals. This book, so ideal for self-study, helped me understand those basic concepts I was lacking!!! I highly recommend it for self-study...it is easy to understand and written in a pretty didactic way!
2 people found this helpful
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Alex P. Keaton
5.0 out of 5 stars Excellent supplement
Reviewed in the United States on December 31, 2013
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I found this book extremely helpful while working through chapters 2 and 4 of baby Rudin (along with Schramm's analysis book). There are numerous examples and accessible problem sets. In hindsight, I wish I would have worked through this book prior to taking my first course in analysis. This is also a great little book to work through prior to tackling the first half of Munkres. That it is an affordable Dover edition easily makes it a 5 star book.
6 people found this helpful
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Juan L.
5.0 out of 5 stars The best book for a beginner to learn topology
Reviewed in the United States on January 11, 2020
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A very enjoyable book to learn about the basics of topology. The author explains the subject matter in a very clear language for those who are beginner learners in Topology. I highly recommend it because I was very frustrated in other books.
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Ian
3.0 out of 5 stars Good for mathematicians
Reviewed in the United States on June 27, 2015
Verified Purchase
With all due respect to the late Professor Mendelson, I have struggled with this book. Having said that, I am neither a mathematician nor graduate student of same. I am a professional specialising in theory and am trying to teach myself (with MIT's help) some belated applied maths useful to theory making. For work I have embarked upon recently I am in need of upgrading my knowledge of things like abstract algebra and topology. This is one of the texts I purchased for self-study.

I guess my main gripe is the book is a bit too dry for me. Which led to a lack of clarity on certain topics. I need a bit more flourish of explanation than mere definitions, theorems, examples. Over and over again. But I know, on the other hand Prof M wrote it from his lecture notes, for his students of serious maths. Not for me. So be it. For example, after reading the book through, then pouring over it in selected areas and chapters for weeks, re-visiting things I had not quite grasped, I still cannot tell the difference between a topological space and a topology - other than by theorem definition. Sure, there I can see (X,T) (T being curly T or whatever it is called) is the former, and T itself the latter. But I remain in desperate need of help from an author saying what this means. In clear simple English, preferably.

I am not negative about the book as a whole, for I now know something at least about topology. As opposed to before I bought it and read it - when I knew zilch.

Recommended for mathematical students; not for inquiring minds of applied people like myself who need more gently, gently.
13 people found this helpful
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Amazon Customer
5.0 out of 5 stars Perfect introduction to someone with no topology knowledge
Reviewed in Canada on July 17, 2022
Verified Purchase
The concepts are very thoroughly explained, and I like that the author started with a discussion of metric spaces before moving on to all the corresponding definitions in a topological space (open set, neighbourhood, etc). I would have liked more illustrations of examples to build geometric intuition though. The questions are also very good and help build a strong understanding of the section before, although there are no answers I have been able to find a pdf with all the answers in it for reference.
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5.0 out of 5 stars Tal cual está en la imagen.
Reviewed in Mexico on March 16, 2022
Verified Purchase
Este libro pertenece a la serie de clásicos en la Topología por lo que tenerlo era algo que me atraía. La exposición de los temas es clara y rigurosa a la vez sin ser engorroso ni tampoco excedidamente formal. Llegó en la fecha indicada sin contratiempo alguno.
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Giangiacomo Gerevini
5.0 out of 5 stars Elegante, conciso, originale
Reviewed in Italy on September 18, 2017
Verified Purchase
Un testo di elevata divulgazione, che introduce il lettore con grande scorrevolezza ai concetti fondamentali della topologia. L'apparente semplicità dell'esposizione non deve ingannare: gli esercizi costituiscono una parte integrante di questa “Introduction”, e chi abbia la costanza di risolverli vi troverà molte sollecitazioni originali per acquisire una solida preparazione di base.
One person found this helpful
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R S K
5.0 out of 5 stars Superb Pedagogy!
Reviewed in India on April 19, 2018
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If you like structured thinking with a lot of abstraction thrown around, this is it!
A feast for Math lovers.
One person found this helpful
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Alec
5.0 out of 5 stars This truly is an introduction book
Reviewed in the United Kingdom on December 5, 2014
Verified Purchase
If you are doing a module in metric spaces or topology you ought to read this, cover to cover ('cept maybe the first chapter, but this is always the case! Chapter 0 is never interesting) in your first or second year, you should know all the content (like the back of your hand) if you are doing a third year module.

It is a brilliant introduction to everything you will need but is just that - an introduction. There's a superb amount of "hand-holding" in the proofs which I found really useful to boost my confidence, after that I'd start covering proofs and then checking them. This is good!

I completely recommend this book, but I do not recommend it is your only topology book (There is another also called "Introduction to topology" with a blue over and an orange torus on the front, from Dover, this is not an introduction it is much more filled out and much faster, if you combine these two, with Munkres' Topology you're set)

There is one thing I don't quite like, the treatment of Quotient topologies (or identification topologies) is rather weak and hard to understand, but I cannot write off a brilliant book due to an iffy 5 pages.

I have no hesitation in recommending this book. I adore Dover because of the great prices also, I am getting quite the collection!
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