Exploring Topology: Follow-up to My PhysicsForums Thread

[Chaostamer]

A follow-up of sorts on my https://www.physicsforums.com/showthread.php?t=457248".

I've decided that, barring any technicalities that prevent me from getting a necessary override, I'm going to definitely take Topology next semester. (I need an override because Topology requires Linear Algebra II as something of a "mathematical maturity" prerequisite. However, with my experience in Combinatorics and Theory of Computation, I think I can get away with taking Linear Algebra II the same semester as Topology.)

Anyway, like I mentioned in my earlier thread, the course is being taught out of C. Wayne Patty's Foundations of Topology. Does anyone have any experience with this book? I'm curious to hear how positively it's regarded, since there don't seem to be many opinions circulating around the review-aggregating sites.

Also, I know that Munkres' book is considered the "bible" of undergrad point-set Topology. I've been considering buying the book to have some extra perspective, since I'm pretty sure Topology's going to be...challenging. For those who have experience with it, would it be a worthwhile purchase alongside Patty's book? If not, is there another book that might serve as a good companion?

As always, thanks in advance to those who help me out.

 

[micromass]

I took a look at "Foundations of topology" and it seems quite good. Of course, Munkres covers more topics (and it is about 200 pages longer...), but this book seems to be good for a one-year course. I don't really see a need to buy another book...

A book that could come in handy is "Counterexamples in topology" by Steen and Seebach. It's not really a textbook, but it covers some interesting and fun counterexamples in topology. I'd say that this book is a must for anybody who is serious about topology...

 

[mathwonk]

I myself read the first few chapters of kelley's general topology and never felt the need for anymore topology short of algebraic topology.

 

[Chaostamer]

I took a look at "Foundations of topology" and it seems quite good. Of course, Munkres covers more topics (and it is about 200 pages longer...), but this book seems to be good for a one-year course. I don't really see a need to buy another book...

A book that could come in handy is "Counterexamples in topology" by Steen and Seebach. It's not really a textbook, but it covers some interesting and fun counterexamples in topology. I'd say that this book is a must for anybody who is serious about topology...

I'm not sure whether I can call myself "serious" about Topology just yet, but I do want to learn the material--at least at an introductory level. Will Counterexamples in Topology help with my grasp of the material in a first course of general Topology?

 

[fourier jr]

p.228 of the Munkres book has a pretty big chunk of everything in the counterexamples book as an exercise, so by that point it might be handy to have. For someone who has never seen topology before except maybe metric spacs I would say it's probably not necessary.

btw I had a look at that book from the op & I think it looks pretty good too.