Elementary Topology Course: Texts, Resources & Suggestions

[Coto]

I have a course on this in the following year and was just wondering what kind of texts are useful for a course on elementary topology. The course description is this:

"Set Theory, metric spaces and general topology. Compactness, connectedness. Urysohn's Lemma and Tietze's Theorem. Baire Category Theorem. The Tychonoff Theorem. Homotopy and covering spaces. Primarily intended for third and fourth year students with a good background in Mathematics."
Suggested text: John G. Hocking's Topology

Any suggestions as to added resources would be appreciated. Thanks in advance.

 

[quasar987]

A classic topology text is Munkres' "Topology".

 

[Gott_ist_tot]

I would read Munkres with the lecture notes on ocw.mit.edu. This helped me in my topology course. It covers everything in your list very well. Be warned, Munkres is a book for mathematicians. If it is one of your first classes outside of calc, linear algebra and the like, then rejoice! It is a phenomenal book. Don't get discouraged and remember it is a tough book but you will understand topology very well with work. Have fun in topology it was one of my favorites.

 

[Cincinnatus]

I thought Hocking's book that you mentioned was actually very good. It's also a dover book so it could be about 1/10 the price of Munkres depending on where you look.

 

[Coto]

Yea, it was the fact that it was a Dover book that put me off unfortunately. I had a bad experience with a couple of Dover's books on Tensor Analysis.. It was actually a combination of those books with a terrible prof that made the experience bad in all. Perhaps then, this is just worry that I'll be put in a similar situation for topology.

Thanks for all the suggestions. We'll see how the class goes based off of those two texts and those online course notes.

 

[mathwonk]

the classic book on topology by hocking and young is an example of a good standard text that is totally out of date. th material is correct and important, but one does nbot learn there to think in mapping theoretic or categorical terms, which is ubiquitous today in virtually every field.

if hiockings book is similarly old fashioned i would supplement it with a more modern book.

 

[Cincinnatus]

I think we are talking about the same book, My post referred to Hocking and Young's book at least...

 

[mathwonk]

well its a good old book, but it is definitely old. for example, after they define singular homology, or maybe homotopy, and prove it is a functor, they prove it is a topological invariant.

but this is trivial from the modern point of view, i.e., all functors preserve isomorphisms.

 

[Cincinnatus]

Ah well, I have only a rather sketchy understanding of category theory anyway... Hopefully that will change next semester when I will (probably) take algebraic topology, I believe that class uses Hatcher's book, which I've heard good things about.

I see here that Hatcher's book is free online!
http://www.math.cornell.edu/~hatcher/AT/ATpage.html

I see he starts the first chapter talking about functors in that book...

 

[mathwonk]

however most of the point set topics in your syllabus are probably not covered by hatcher. hocking is a good book for that stuff, just old.