Book Suggestions for Undergraduate Topology Class

[cap.r]

Hello, I am taking my first Under graduate topology class and the class is using Topology by Munkres it's a great book and he has done a good job with explaining things.

but I always like to read from at least two different books and see more examples before I try the homework or convince myself that I know the material.

so any suggestions?

The chapters we will be doing are :
2 Topological Spaces and continuous Functions
3 Connectedness and Compactness
4 Countability and Separation Axioms
9 The Fundamental Group
10 Separation Theorems in the plane
12 Classification of Surfaces
13 Classification of Covering spaces

the last two might not happen if we don't have enough time...

the prof. also recommended Basic Topology by M.A. Armstrong as a secondary reference. but I thought I would check it out before I purchased that one.

thanks,
RK

 

[Petek]

Looks like your course could be described as an introduction to topology/algebraic topology.

The Armstrong book has been used at UC Berkeley for just such a course, so it should be a nice secondary reference. This year, however, https://www.amazon.com/dp/0521298644/?tag=pfamazon01-20 by John Lee. It covers approximately the same material as Munkres at about the same level. You might look for some or all of these books in your library to see if one or more of them suits you.

HTH

Petek

 

[rasmhop]

I recently acquired General Topology by Stephen Willard and really like it. It's a general topology book so you may not find a lot of stuff on covering spaces or classification of surfaces in it (it does have a couple of sections on the fundamental group though, and some intro to covering spaces in the exercises). Anyway it nicely complements Munkres and is pretty cheap so I thought I'd mention it. I haven't read the book by Armstrong so I don't know how this one compares. I would also like to second the recommendation of Introduction to Topological Manifolds. It has most of what you want, and in my opinion it does a slightly better job of preparing you for subsequent algebraic topology courses than Munkres.