> Do the problems in Munkres' topology, but only up to Metrization theorems
Related: My stackexchange question https://math.stackexchange.com/questions/2780653
1. Is the coverage really up to metrizations, which is Chapter 6 (as far as you know/in your experience/from your understanding/from what you've heard/pick any similar phrase you like)?
I believe the content in Chapters 1, 2 and 3 are part of the GRE coverage. My question is mainly about chapters 4,5 and 6.
2. What are the relevant chapters in Part II of Real Analysis by Royden and Fitzpatrick? (table of contents is in the stackexchange question linked above) I'm guessing Chapters 9 - 12.
Update: Based on https://www.mathsub.com/resources it looks like the coverage is as follows:
So it's up to Chapter 7 of Introduction to Topology: Pure and Applied by Colin Adams and Robert Franzosa? Is that including quotient topology? In Munkres, it's a starred section...Introduction to Topology: Pure and Applied by Colin Adams and Robert Franzosa
Not only do Adams and Franzosa give clear presentations and explanations of the definitions in point-set topology, but they provide plenty of illustrated geometric examples from both familiar and unfamiliar spaces, more than I’ve seen in many other books on the subject. The first half of the book is really all you need to be ready for the Math Subject Test, and while the exercises are more on the proof-heavy side, they’re certainly doable.
Update: I studied all sections in Chapters 2 and 3 except the starred sections. I didn't do the exercises in Section 19 and don't plan to. I don't plan to do the exercises in Sections 28 and 29. I think Sections 28 and 29 are beyond the score of the GRE, but only a little beyond. I studied or plan to study the exercises in the sections of Chapters 2 and 3 except the starred sections and except Sections 19, 28 and 29. My plan is based on that up to Chapter 7 of Introduction to Topology: Pure and Applied by Colin Adams and Robert Franzosa seems to be the coverage for the GRE and these seem to correspond with up to Chapter 3 of Munkres, unfortunately including Sections 28 and 29, but I think I'll take my chances.