Choosing a text for a First Course in Topology

Question

Which is a better textbook - Dugundji or Munkres? I'm concerned with clarity of exposition and explanation of motivation, etc.

Answer 1

Try Simmons, Introduction to Topology and Modern Analysis.

Answer 2

As BBischof says: Willard is nice. I also learned a lot from Mendelson, a little dover book. I think that you should use whatever gets you through the subject "quickest". Point Set topology is now just basic language that is very necessary, but it seems there is not much research in the field.

My dad did not go into math because of a course out of munkres, he had no intuition for the topic the way it was taught. I dont see this as a criticism of Munkres because I think one of the major goals of any early course is to untrain the student. There are spaces that are pathological that you have to deal with. You have to be rigorous. I think that is one of the main points of such a course, that and preparing the student for what comes next. Which is why mariano asks what your goals are.

One thing about willard though is that you should make sure you do the exercises, they contain key facts!

Edit: I felt it pertinent to add that I did go through a course from munkres (by the time I did it was pointless for me, I had already been using the relevant stuff for my field daily) and it was quite well done I thought. It is the classic, I don't think you can go wrong with it.

Answer 3

Good and Free

Topology Without Tears by Sidney A. Morris

Answer 4

Sutherland's Metric and topological spaces is nice. I know a guy who swears by Kelley's General topology but I've not read it myself.

Answer 5

I would like to recommend Topology: Pure and Applied, by Colin Adams and Robert Franzosa. Anyone familiar with Colin Adams's The Knot Book will expect this to be equally accessible. And they will not be disappointed. In terms of your criteria—clarity and motivation—I find it unsurpassed.

Answer 6

I think Munkres' is a great book, though you can safely skip some sophisticated counter-examples in it.

Janick's "Topology" is more intuitive, less technical or just less narrowly focused on the specific subject of Topology -so it links to other parts of mathematics. But I've never dared to base my lectures on it, precisely because elementary Topology can be explained on its own, out of the blue, without assuming any previous knowledge at all, whereas mixing it with Differential Geometry, for instance, can be more confusing than useful for undergraduate students.

Nevertheless, Janick's book has some masterpieces; for instance, the proof of Urysohn's lemma: the first time I read it I realised that there are people in this world who actually understand maths, and others, well... we just repeat, more or less succesfully, what we have learnt (or so we hope). The same proof in Munkres' simply doesn't compare.

As for Dugundji, it's a great book, but nowadays it seems to me much too difficult for undergraduate students.

Answer 7

I learned point-set topology from Munkres and absolutely loved it. It is probably one of the most worn books I own. For an introduction to topology with a more geometric/algebraic feel to it, I highly reccommend John M. Lee's Introduction to Topological Manifolds. He provides sufficient, but no more, point-set topology to support the algebraic developments. His proofs are very clear and on par with Munkres in this regard.

Answer 8

Topology For Beginners by Steve Warner It starts with Set theory and goes from there. It ends with Algebraic topology

Answer 9

I have saw both texts you mentioned. I’d go for Munkres. Even the Math Sorcerer Chanel say it is the standard to learn from. It is like Spivak’s Calculus to learn analysis.I learnt analysis from Spivak,I could not stand the text.

Personally, I like Principles of Topology by Fred Croom. You can see the whole text at archives.org. Proofs are shown for many theorems and the book is nicely laid out.Principles of Topology