Which book to use in conjunction with Munkres' TOPOLOGY, 2nd edition?

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?

Solution 1:

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.

Solution 2:

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.

Solution 3:

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.

Solution 4:

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 ....

Solution 5:

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.