Supplement book for topology

I am taking a course in topology with Gamelin and Greene, Introduction to topology. I would like to have some supplement to extend and give more motivation and explanation. I am quite tired of the "theorem, proof, theorem, proof" pattern.

Thank you!

Solution 1:

My recommendation is to not restrict your search to a single book for a supplement, but rather assemble several similar books and use all of them. Something in one book might not make sense, then you read about the same topic in another book and you understand the topic, and then, amazingly, when you look back at the first book again you find that the treatment of the topic in the first book gives, for you, the better treatment --- you simply needed some mental nudging from the second book in order to “read what had originally been a Foreign language to you” in the first book. Of course, for someone else, both books might be opaque on the topic, and a third book will work for that person. Most often, however, is that you pick up some understanding on the topic from each of several books, and when you assemble together what all the books say on that topic, then you mostly understand it. (Note: To go from “mostly understand it” to “understand it very well”, find someone in your class who doesn’t understand it and explain it to them! Or search Mathematics Stack Exchange for a question on the topic and write an answer that broadly explains the topic.)

In today’s world, in which students rarely check out university library books, there should be plenty of appropriate topology books sitting on the library shelves --- look for such books around the QA 611 location, if your library uses the U.S. Library of Congress classification. Things were quite different when I was in college, by the way. Then, whenever a topology class was being offered, most of the better known undergraduate and beginning graduate level texts would be snapped off the shelves within the first few days of class, and similarly for other classes in advanced specific areas.

I just looked at my copy of Gamelin/Green (1999 2nd edition) to get an idea of its level. Below are some books that seem to fit the best (i.e. I’m skipping Kelly, Dugundji, Wilansky, Gaal, Cullen, Munkres, Engelking, Willard, Thron, Schubert, Pervin, etc. level books), at least for the first two chapters. (Chapters 3 and 4 of Gamelin/Green deal with homotopy theory.) The first 5 books are from my bookshelves, the next 4 books I know about but don’t actually have in front of me right now, and the 4 remaining books are those I found by looking at the amazon.com suggestions. There are likely many more books that could be useful that your library might have, because books mentioned by people online are typically rather recent (or recently have been reprinted by Dover Publications), and many older gems will be overlooked if you only rely on superficial online searches. A non-superficial search would be to look at the bibliographies of all the books you can get a hold of, but since you probably have very limited financial funds, this won’t do much good unless the books you find out about are actually in the library, so this is another reason to look there --- everything you see will definitely be something you can make use of for free.

Undergraduate Topology. A Working Textbook by Aisling McCluskey and Brian McMaster (2014)

Undergraduate Topology by Robert H. Kasriel (1971/2009)

For what it’s worth, this is the book I used for my first topology course (an independent reading course), and this 28 March 2006 sci.math post gives some of my thoughts on the book.

Fundamentals of Topology by Benjamin T. Sims (1976)

Schaums Outline of General Topology by Seymour Lipschutz (1965)

Introduction to Topology by Bert Mendelson (1975/1990 3rd edition)

Topology by K. Jänich (1984)

Theory and Examples of Point-Set Topology by John Greever (1967)

Principles of Topology by Fred H. Croom (1989/2016)

Introduction to Topology by Crump W. Baker (1991)

An Illustrated Introduction to Topology and Homotopy by Sasho Kalajdzievski (2015) [see Solutions Manual also]

Understanding Topology: A Practical Introduction by Shaun V. Ault (2018)

Introduction to Topology. Pure and Applied by Colin Adams and Robert Franzosa (2007)

Elementary Point-Set Topology by Andre L. Yandl and Adam Bowers (2016)

Solution 2:

Munkres-Topology book is a nice book. It gives good intiution I think. I haven't studied various topology book so Munkers is only one I can recommend but anyone studied Munkres likes it