A general topology textbook for a specific purpose and taste, from a specific set of choices

Question

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.

Answer 1

You won't like Willard, it's for serious students of point set topology with little devoted to spaces analyists use.

Answer 2

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.