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This answer suggests to do Munkres Topology for the GRE Subject Test in Mathematics: recommending books for GRE math subject test

1. Up to approximately which chapter is needed for the GRE?

Of course only ETS can say for sure. But I believe those who have studied topology will be able to have a good guess.

2. I just found out that Real Analysis by Royden and Fitzpatrick has sections on Topology. What's the difference between their sections and Munkres Topology?

I mean, is one more detailed than the other? Could Royden and Fitzpatrick Real Analysis' sections on Topology perhaps suffice for the GRE?

I guess Munkres Topology is broader or more detailed while Royden and Fitzpatrick cover the parts needed for real analysis or something.


For reference, here are the tables of contents:


Munkres Topology

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Real Analysis by Royden and Fitzpatrick

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    $\begingroup$ they're both overkill but if I were you I would use Royden's sections. an old guide I have reads, "-Do the problems in Munkres' topology, but only up to Metrization theorems (As many as time permits)" $\endgroup$ – Tony S.F. May 24 '18 at 18:36
  • $\begingroup$ @TonyS.F. Re sentence 1: I wish you're right. What makes you say that please? Re sentence 2: Found it. Thanks. To clarify, you disagree? $\endgroup$ – BCLC May 24 '18 at 18:54
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    $\begingroup$ Taking the subject test twice is what informs my decision. $\endgroup$ – Tony S.F. May 24 '18 at 20:09
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    $\begingroup$ The book Real Analysis by Royden & Fitzpatrick can be divided into three parts, real analysis, topology, and measure theory. I have taken two courses which are real analysis and measure theory respectively, and the textbook of both of them are this book. As for me, I will choose this book, since these two parts are very good. Unfortunately, I never read the topology part of it, but I am convinced it will be not bad. This book has a lot of typos, you can find the list of typos on google. But some typos need to be found by yourself, which is also a process of studying. Anyway, I recommend it :) $\endgroup$ – Sam Wong May 25 '18 at 8:51
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    $\begingroup$ I have a glance at the contents of this book. It seems having no the fundamental group stuff and something else related algebraic topology. But the other book has. I don’t know what extent of knowledge GRE sub requiring, but the book by Munkres may give you a broader view about topology. I don’t know you are preparing for GRE or GRE sub. As for GRE, its math part is easy, and I think it will not need the knowledge of topology. As for GRE sub, you can take the book by Munkres. Because the second part of the book by R & F, has more flavor of functional analysis. $\endgroup$ – Sam Wong May 25 '18 at 9:02
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In my opinion, they are both overkill. I took the exam twice having taken a course in topology (mostly geometric stuff like classification of surfaces) and I didn't feel lacking. The focus should be primarily on vector calculus anyways since the majority of the test is on this subject.

There is this guide and it is well put together, but probably a bit overkill. I would agree that it's a good idea to do the problems up until metrization if you have time, certainly some topology problems are directly on the test and some problems can be more quickly solved using topology so it doesn't hurt, it's just more work.


From comment:

they're both overkill but if I were you I would use Royden's sections. an old guide I have reads, "-Do the problems in Munkres' topology, but only up to Metrization theorems (As many as time permits)"

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  • $\begingroup$ From comment: they're both overkill but if I were you I would use Royden's sections. an old guide I have reads, "-Do the problems in Munkres' topology, but only up to Metrization theorems (As many as time permits)" $\endgroup$ – BCLC May 26 '18 at 14:32
  • $\begingroup$ Tony S.F., for Munkres: is the coverage really up to metrization, i.e. up to Ch6, as far as you know? For Royden Fitzpatrick: what are the relevant chapters in Part II? I'm guessing Ch-9Ch12. $\endgroup$ – BCLC Sep 14 '18 at 8:41
  • $\begingroup$ I would say it's a crap shoot at that point. You might get a version of the exam that is almost entirely algebra/number theory/combinatorics for the special subjects. $\endgroup$ – Tony S.F. Sep 14 '18 at 16:49
  • $\begingroup$ that's fine. I'm more interested in studying for the topology topics covered in the GRE than the topology part of the GRE. In your gen topology course what was the last topic? $\endgroup$ – BCLC Sep 14 '18 at 23:35
  • $\begingroup$ Singular homology of surfaces. It was a unique first topology class in that we, the students, chose what to look at and we spent a lot of time on geometric concepts like classification of surfaces rather than more analytics topcs. $\endgroup$ – Tony S.F. Sep 17 '18 at 9:41

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