What Topology Book Should I Start With Given My Background?

[JonF]

I’m looking for a recommendation for a topology book that I could go through myself. I’ve been told that I should learn point-set topology before algebraic topology, but my algebra is much stronger than my analysis – so I’d also like to know if point-set necessarily comes first.

I’ll give my background of all of the courses I think might be relevant so you can judge the level of text I’m ready for:2 semesters of linear algebra , 2 semesters of real analysis, 1 of complex analysis, a course in non Euclidian geometry, 2 semesters of abstract algebra, 1 of galois theory, number theory, and a course on set theory.

 

[xepma]

I liked Munkres -- Topology:

https://www.amazon.com/dp/0131816292/?tag=pfamazon01-20

as an introductory. Covers a lot of topics, is rigorous and moves to Algebraic Topology the final 1/3rd of the book --although you might want to consider a different book devoted to this particular subject.

Have to admit that I did not go through any other Topology books.

 

[mathwonk]

a nice well written one accessible even to strong high school students, and yet by a great expert in topology, is "first concepts of topology" by chinn and steenrod.

pure point set topology is sort of a trivial subject, and when divorced from applications to maps of circles and spheres and other real life examples, gives an unfortunate lack of feel for the basic idea, namely continuity.

a book like kelley's "general topology" has that complete lack of geometric feel, and was apparently meant as a handbook for analysts, rather than geometers or topologists. the deep side of topology is its connection with differential calculus and geometry. good books for the former include that by guillemin and pollack.

still one can learn the basic trivial definitions from the first few sections of kelley. munkres is probably excellent, and is widely recommended for students, but i have not read it.

 

[xristy]

I have a fondness for Hocking and Young Topology. It's available in Dover reprint and covers point-set topology, homotopy, homology and knot theory at a level that is suitable for getting a handle on the ideas but not with all the more modern and abstract machinery. It's a "good read".

 

[JonF]

Thanks guys, I ordered Munkres.