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Does anyone know of a good topology textbook, that has a solutions manual for at least some of the problems? Older is fine; I just need to be able to check my own work.

I've researched best topology books/free topology books, but most do not have any solutions to problems provided.

Thanks for your help; hope I'm posting in right forum.

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  • $\begingroup$ I think Bert Mendelson's intro to topology is a rudimentary but very easy read. It doesn't have the solutions, but the questions are easy enough to work out with no prior knowledge (other than perhaps some nonaxiomatic set theory). $\endgroup$ – parsiad Dec 30 '15 at 18:53
  • $\begingroup$ Did you have look at other posts tagged general-topology+book-recommendation? For example, this one seems rather similar: Topology Exercises Books, $\endgroup$ – Martin Sleziak Dec 31 '15 at 13:19
  • $\begingroup$ There are many topology books with different approaches and focuses. Many of the older books (that are cheaper) focus on topics that you may not need. You can get better answers by explaining what you want to get out of your topology course. $\endgroup$ – Carl Mummert Dec 31 '15 at 13:29
  • $\begingroup$ Judging from my students turned-in work, virtually all of the problems from Munkres's "Topology" have solutions on-line in various fora. $\endgroup$ – Cheerful Parsnip Jan 1 '16 at 5:42

10 Answers 10

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Munkres' topology book is quite standard. Although I don't think he has an official solutions manual, many solutions exist online.

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you can read munkres it's a good book ,there are solutions online on http://dbfin.com/topology/munkres

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Elementary Topology Problem Textbook

O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov

Great book, with many easy problems, and with basically everything solved at the end of each chapter.

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During my student years I used and liked General Topology by Stephen Willard. It has a solution manual by Jianfei Shen.

Also interesting: General Topology by John L. Kelley.

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Take this alternative choice Topology Without Tears

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Introduction to Topology: Pure and Applied is a really neat book. The author explains concepts clearly and includes easy to follow proofs and theorems. Also, as the title suggests, there are some sections on the applications of Topology, including some cool stuff like Cosmology, Knots, Dynamical Systems and Chaos. You normally don't see that in the standard Topology textbook.

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"Introduction to Topology" of Gamelin. Highly readable. It contains solutions of some selected problems at the end.

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  • $\begingroup$ This is the same book which was already suggested in another answer, right? $\endgroup$ – Martin Sleziak Dec 31 '15 at 18:20
  • $\begingroup$ Yes, but at the time I posted my answerr, I didn't aware of it. $\endgroup$ – SiXUlm Dec 31 '15 at 19:06
  • $\begingroup$ Are there any solutions for exercises online except the solutions the book itself? I find some of the "solutions" that Gamelin has are non-trivial. $\endgroup$ – Ninja May 12 '17 at 19:55
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"Counterexamples in Topology" by Lynn Arthur Steen and J.A. Seebach

"According to the authors of this highly useful compendium, focusing on examples is an extremely effective method of involving undergraduate mathematics students in actual research. It is only as a result of pursuing the details of each example that students experience a significant increment in topological understanding. With that in mind, Professors Steen and Seebach have assembled 143 examples in this book, providing innumerable concrete illustrations of definitions, theorems, and general methods of proof. Far from presenting all relevant examples, however, the book instead provides a fruitful context in which to ask new questions and seek new answers.

Ranging from the familiar to the obscure, the examples are preceded by a succinct exposition of general topology and basic terminology and theory. Each example is treated as a whole, with a highly geometric exposition that helps readers comprehend the material."

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My course used Introduction to Topology by Gamelin and Greene; http://www.amazon.com/Introduction-Topology-Second-Edition-Mathematics/dp/0486406806. It's a little bit harder then Munkres but doesn't beat around the bush! You need to know some non-trivial set theory tho before starting. It has some solutions/hints and cost almost nothing.

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  • $\begingroup$ Are there any solutions for exercises online except the solutions the book itself? I find some of the "solutions" that Gamelin has are non-trivial. $\endgroup$ – Ninja May 12 '17 at 19:55
  • $\begingroup$ @Ninja not as far as I know. $\endgroup$ – user1 May 12 '17 at 20:04
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The best textbook in my opinion is Munkres' book. It's a balance between rigour and simplicity. You can find the solutions to the exercises everywere on internet.

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