What are the best books on point set topology for undergraduate students?

[R.P.F.]

Hi! Can someone recommend some books on point set topology for undergraduates? I am going to use it this summer for preview and also during the fall because the instructor is not going to use a textbook. Thank you!

 

[hitmeoff]

A very cheap way to go is Mendelson's "Introduction to Topology." I used it a lot last quarter to supplement another text. I am an undergrad and took undergrad topology, but we officially used a grad level book, which was to say the least...very dense. So the Mendelson book expanded on a lot of the topics we covered.

Im am sure there are better/more modern treatments of topology out there for undergrads (I believe Munkres is the standard, but I don't have it). But the Mendelson book is so cheap, you should get it anyway. If its not to your liking, then who cares since you never invested much on it.

 

[micromass]

Hi R.P.F.!

I can highly recommend Munkres! It's one of the best topology books out there. It's really made for somebody's first encounter with topology. It doesn't only explain things in a lot of details, but it also goes quite deep into the topology!

Another book that every serious topology student should have is "Counterexamples in topology" by Steen and Seebach. It's not a textbook and it's a bit older, but it contaisn all the quirky and weird counterexamples in topology. If you ever start wondering if there exists a separable compact space that is not connected? Check this book and find out!

My favorite topology book is "General topology" of Willard. But I wouldn't recommend it to beginning students. It might be a bit dense...

 

[vici10]

Engelking's book "General Topology" is probably the most comperhensive book on set-theoretic topology. It maybe an overkill for an undergraduate level, but it is also can be used as a reference. Unfortunately, the book is out of print. But you can find it on the net.

 

[qspeechc]

Hi R.P.F.!

I can highly recommend Munkres! It's one of the best topology books out there. It's really made for somebody's first encounter with topology. It doesn't only explain things in a lot of details, but it also goes quite deep into the topology!

Another book that every serious topology student should have is "Counterexamples in topology" by Steen and Seebach. It's not a textbook and it's a bit older, but it contaisn all the quirky and weird counterexamples in topology. If you ever start wondering if there exists a separable compact space that is not connected? Check this book and find out!

My favorite topology book is "General topology" of Willard. But I wouldn't recommend it to beginning students. It might be a bit dense...

We used Willard for our undergrad course. We had a great instructor too, but at some points I found Willard clearer even than him. The exercises are really meaty and challenging. I think it's great, cheap too. If you struggle with it there are plenty of Dover books on topology, maybe have a look at them in the library or on the web, and pick two or three. It will turn out far cheaper than Munkres (which I have not read).

Also, it seems to me comparing their contents, Willard covers a lot more general topology stuff, but Munkres covers less and moves on to algebraic topology in the 2nd part of the book. The general topology stuff may be better for future analysts, and algebraic for everyone else. If you can get a cheap used copy of Munkres, maybe getting both is a good way to go.

 

[R.P.F.]

Thank for for all the suggestions! I read a little bit of Munkres' Elements of Algebraic Topology. It's kind of out of date. But I will read his Topology since everyone recommends it.