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Although Topology by James R. Munkres, 2nd edition, is a fairly easy read in itself, I would still like to know if there's any text (or set of notes available online) that is a particularly good choice to serve as an aid to Munkres' book, in case one gets stuck in some place in Munkres or in case one need to suggest some supporting text to one's pupils.

I know that there's a website where solutions to some of Munkres' exercises are also available.

Is the book Introduction to Topology and Modern Analysis by Georg F. Simmons a good choice for this same purpose?

Or, is Introduction to Topology Pure and Applied by Colin Adams a good companion to Munkres?

And, what about the General Topology text in the Schaum's Series?

P.S.:

Thank you so much Math SE community! But I also wanted to ask the following:

Which book(s) are there, if any, that support Topology by James R. Munkres, 2nd edition, in the sense that they cover the same material as does Munkres; prove the same theorems as are proved in Munkres, but filling in the details omitted by Munkres; use the same definitions as used by Munkres; include as solved examples some, most, or all of Munkres' exercise problems?

Of course, one cannot expect a text to fulfill all the above requirements, but which one(s) do(es) this the best?

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  • $\begingroup$ We have Armstrong's Basic Topology and i bought the general topology book in the Schaum's series too. It arrived yesterday and so far im not happy with it. I can give a more detailed reply in a couple of days. You can also look here for advice: [enjoyable book to learn topology] math.stackexchange.com/questions/573781/… $\endgroup$ – JKnecht Jan 26 '16 at 21:44
  • $\begingroup$ If I could add a recommendation against, it would be the above-mentioned "Basic Topology" by Armstrong. This is the book out of which I first learned the subject, and I found Munkres' approach much more enjoyable. Meanwhile, If your desire is to complement Munkres' treatment, then you might see if you can find a text that broaches topology from the perspective of closed sets rather than open ones; this is sometimes done in terms of the Kuratowski Closure Axioms... $\endgroup$ – Benjamin Dickman Aug 24 '17 at 4:56
  • $\begingroup$ @JKnecht can you please have a look at my post? I've just added a P.S. $\endgroup$ – Saaqib Mahmood Sep 3 '17 at 17:17
  • $\begingroup$ @BenjaminDickman I've tried being more specific in what I need to know by adding a P.S. to my post. So can you please answer my P.S. query too? $\endgroup$ – Saaqib Mahmood Sep 3 '17 at 17:19
  • $\begingroup$ @MarkusScheuer can you please also answer to my specific query in the P.S. part of my post, which I've just added? $\endgroup$ – Saaqib Mahmood Sep 3 '17 at 17:20
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The following book was (and still is) a valuable resource together with Munkres Topology:

Aspects of Topology by C.O. Christenson and W.L. Voxman is an easy to read, instructive text about general topology containing a lot of nice graphics.

This AMS review might be useful.

In addition and independent to text books as above I would like to put the focus on:

Counterexamples in Topology by L.A. Steen and L.A. Seebach. This is a great resource to look for topological spaces having specific properties and to look for topological properties and their relationship. It contains extensive charts of terms like compactness and the relationship of their different flavors. See also this Wikipage.

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    $\begingroup$ +1 for Steen and Seebach. Many courses assign it as a supplementary text. It should just be noted that their notation is sometimes a bit out of date, and in particular doesn't always match Munkres. $\endgroup$ – Nate Eldredge Aug 23 '17 at 16:52
  • $\begingroup$ @NateEldredge: Thanks for upvoting! I remember many years ago when I did my first steps into general topology this book was a revelation for me. I was overwhelmed about the many different variations of compactness which impressively demonstrated its importance. ... and these many, many wonderful examples of topological spaces ... :-) $\endgroup$ – Markus Scheuer Aug 23 '17 at 17:02
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Two recently published books that I have used (actually instead of Munkres) include:

  1. Topology by Manetti: http://www.springer.com/gp/book/9783319169576.
  2. Topology: An Introduction by Waldmann: http://www.springer.com/gp/book/9783319096797.
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I'm fond of Introduction to Topological Manifolds by Lee. It's about halfway between Munkres and Hatcher in terms of content, and filled with examples. It also acts as a good prologue for his Introduction to Smooth Manifolds, if you want to see what differential geometry has to offer.

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The Schaum's outline of General Topology is the best book ever to learn Topology from .....Munkres' is difficult to learn from, because like most American Math Texts, it does not have enough worked out examples ...This is a rather difficult subject to learn without a good professor guiding the learner...However one small advantage that Munkres' has is that one can find solutions to some of the exercises online (because it is a widely used book) , so you can check your work (sometimes ) if you are doing the exercises by yourself... I would not recommend the other books you mention ....

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I really liked the book Elementary Topology. Textbook in Problems by Viro, Ivanov, Kharlamov and Netsvetaev as a companion to Munkres. It is based on topology classes at the Faculty of Mathematics and Mechanics of the Leningrad State University in the 1980s.

As the title suggests, the greatest portion of the book is made up of problems, exercises and examples, which are great for absorbing the material.

Furthermore, the online version is available for free in the author's webpage. Note that the online version does not include proofs or solutions to exercises, but it's great as a problem book. Even better if you have some fellow students to discuss some of the problems with, so you can help each other out if you are stuck and compare proofs.

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I suggest Essentials of Topology with Applications, by Steven G. Krantz (CRC Press), who writes very well. Besides, of course, the references to applications of Topology,which are not very common in Topology textbooks.

I would also have suggested Counterexamples in Topology, had not someone alse suggested the same book too.

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