Can anybody recommend me a topology textbook? [duplicate]

Possible Duplicate:
choosing a topology text
Introductory book on Topology

I'm a graduate student in Math. But I never learnt Topology during my undergraduate study. Next semester, I am going to take Differential Geometry. I assume this course would require a background of Topology. So I would like to take advantage of this summer and learn some topology myself.

I don't need to become an expert in Topology. All I need is that after this summer, my topology knowledge will be enough for my Differential Geometry course.

So can somebody please recommend me a textbook? I'd be really grateful!

Solution 1:

Munkres Topology is a magnificent book. It is well written and covers the basics of point set and elementary geometric topology extremely well. I agree with William.

Solution 2:

Seebach and Steen's book Counterexamples in Topology is not a book you should try to learn topology from. But as a supplemental book, it is a lot of fun, and very useful. Munkres says in introduction of his book that he does not want to get bogged down in a lot of weird counterexamples, and indeed you don't want to get bogged down in them. But a lot of topology is about weird counterexamples. (What is the difference between connected and path-connected? What is the difference between compact, paracompact, and pseudocompact?) Browsing through Counterexamples in Topology will be enlightening, especially if you are using Munkres, who tries hard to avoid weird counterexamples.

Solution 3:

I entered my graduate general topology course with no previous background in the field (save what I knew about the real line). Despite this, I had great success with Stephen Willard's General Topology.

Solution 4:

Crossley's Essential Topology gives a slightly more elementary introduction than Munkres, and driven more by examples than by theory. I found it useful when I got stuck with Munkres.

http://www.amazon.com/Essential-Topology-Springer-Undergraduate-Mathematics/dp/1852337826

Solution 5:

I know a lot of people like Munkres, but I've never been one of them. When I read sections on Munkres about things I've known for years, the explanations still seem turgid and overcomplicated.

I like John Kelley's book General Topology a lot. I find the writing stunningly clear. It has been in print for sixty years. You should at least take a look at it.