Subject: Re: topology text Date: Tue, 3 Apr 2001 14:33:41 -0400 From: Allen Hatcher To: Don Davis On the subject of undergraduate point-set topology texts: At Cornell we have used Munkres' book for a number of years, and my impression is that it is used at many other places as well. It seems serviceable, students like it, and it covers plenty of material. Personally, I can't generate much enthusiasm for it since it seems too long-winded (a virtue for many students) and seems to chop everything up into too small pieces. (Shostakovich made a similar comment about Toscanini's conducting.) However, that's just my opinion, and apparently many other topologists like the book. A more objective issue is the one of cost. The new edition of Munkres' book is in the $90 range, which seems totally unjustifiable. If it were published by Springer as an undergraduate text it would be around half that, and other publishers such as Cambridge would do it for even less. How can Prentice-Hall justify this price? Closer to home, how can we justify choosing books like this? It seems to me that when we as instructors continue to select textbooks without regard to price, we are just perpetrating this irrational and iniquitous system. It's time to mend our ways. I know one can say an extra $50 is just a drop in the bucket compared to other college costs, but these drops add up, and there's no real justification for them. Climbing off my soapbox, let me mention an alternative text that I used last fall and was reasonably satisfied with. This is Gamelin & Greene's "Introduction to Topology," reissued by Dover for $10. (The students certainly loved the price!) The first chapter is on metric spaces with something of an analysis slant, but the book is written so that this can be mostly skipped in favor of digging into the second chapter, on general topological spaces. The third chapter is on fundamental group, and there is a shorter fourth chapter on higher homotopy groups, culminating in the notion of degree. There is no homology. The overall style is attractive and the students seemed to like the book fairly well. There is a good selection of exercises, nearly all of which have sketched solutions in the back of the book. As a result, I had to come up with lots of alternative exercises. For me this was the main drawback of the book. Two other books I like are Janich's "Topology" and Armstrong's "Basic Topology," although I'm not sure they would do as textbooks for our course. Allen Hatcher