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I'm not much interested in algebraic/differential/geometric topology as I'm more geared towards analysis. A solid foundation for general topology (aka point-set topology) would do for now. I can't decide on which one to choose from these set of three books to meet my purpose. It would be really helpful if anyone can give me a comparative study of these books, their strengths and weaknesses and his/her overall experience (feel free to describe your experience even if you've covered only one or two of these), so I can have a better understanding of what these books offer and whether it fits my bill.

(1) General Topology - Stephen Willard

(2) Introduction to topology and modern analysis - G. F. Simmons

(3) Topology - James Munkres

I prefer the books with lots of remarks, notes, discussion and strong sets of exercises that make me think, over the "facts only, ma'am"-type of dry books. Thanks in advance.

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  • $\begingroup$ Do you mean you can or can't pick one of these three books? If you can't, why are you interested in them? $\endgroup$ – martin.koeberl Apr 3 '17 at 2:06
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    $\begingroup$ Sorry I meant that I want to pick one of them but don't know which one fits my bill the best $\endgroup$ – aditi_ray Apr 3 '17 at 2:07
  • $\begingroup$ Maybe you have done that already, but I'd recommend to look around whether you can find previews (author page/ Google books/ ...) of these, so you can look at the style to see whether you like it. $\endgroup$ – martin.koeberl Apr 3 '17 at 2:09
  • $\begingroup$ I'm not familiar with (1), but I am familiar with (2) and (3). Munkres' book is certainly geared as a 'standard' introduction to topology, which is point-set topology and then elements of algebraic topology, i.e. the fundamental group, surfaces, etc. (2) is certainly geared towards analysis. Simmons is an excellent author, and while I've never studied from his book (just thumbed through it a few times), it's definitely more focused. Simmons tends to write pretty good books though, and a pdf of it is readily available (just google his name), so you might try that out. $\endgroup$ – Alfred Yerger Apr 3 '17 at 2:34
  • $\begingroup$ @AlfredYerger Thank you for your reply. Would you be kind enough to elaborate what you mean by focused? i.e. focused to what? $\endgroup$ – aditi_ray Apr 3 '17 at 2:37
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You won't like Willard, it's for serious students of point set topology with little devoted to spaces analyists use.

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This book is geared at probably a lower level than the ones mentioned, but Mendelson's Introduction To Topology introduces the abstract definitions of a topological space as a generalization of $\mathbb R^n$ and metric spaces in general.

Additionally:

  1. It will give you the requisite subjects to understand the topology necessary for basic analysis.

  2. It is is also very short, which seems important.

I'm only familiar with Munkres, but it is a huge reference text dealing with many topological considerations not immediately necessary for most analysis. I think that Mendelson's book would be a bare-boned introduction, and give you enough inisight to look up, say Urysohn's Lemma, in a larger and more detailed reference text.

Unlike Simmon's there is not so much of a functional analysis bent here, but I think any standard text on functional analysis would cover the basic topological considerations, which will be comprehensible after a reasonable introduction, where you can really learn the topology that you are interested in. In my opinion, this is a better route anyhow, the "deep" general topology did not help me at all with Functional Analysis, learning topology from a functional analysis book did, though.

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