Topology coverage in the GRE

Forum for the GRE subject test in mathematics.
BCLC
Posts: 36
Joined: Mon Oct 24, 2016 1:10 am

Topology coverage in the GRE

Postby BCLC » Fri Sep 14, 2018 4:32 am

This guide https://www.reddit.com/r/math/comments/ ... n/cj6r19f/ says

> 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.

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Update: Based on https://www.mathsub.com/resources it looks like the coverage is as follows:

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.


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...

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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.
Last edited by BCLC on Wed Oct 03, 2018 8:17 am, edited 4 times in total.

djysyed
Posts: 258
Joined: Sat Oct 28, 2017 9:59 pm

Re: Topology coverage in the GRE

Postby djysyed » Fri Sep 14, 2018 6:24 pm

I've taken the MGRE before and I've never seen questions that require knowledge of material beyond compactness and connectedness. Moreover, these were in regards to \mathbb{R}^n and not any general topological space. Baby Rudin chapters 2-4 cover this pretty well.

BCLC
Posts: 36
Joined: Mon Oct 24, 2016 1:10 am

Re: Topology coverage in the GRE

Postby BCLC » Sat Sep 15, 2018 5:50 am

djysyed wrote:I've taken the MGRE before and I've never seen questions that require knowledge of material beyond compactness and connectedness. Moreover, these were in regards to \mathbb{R}^n and not any general topological space. Baby Rudin chapters 2-4 cover this pretty well.


ok thanks =)

BCLC
Posts: 36
Joined: Mon Oct 24, 2016 1:10 am

Re: Topology coverage in the GRE

Postby BCLC » Sat Sep 15, 2018 5:57 am

djysyed wrote:I've taken the MGRE before and I've never seen questions that require knowledge of material beyond compactness and connectedness. Moreover, these were in regards to \mathbb{R}^n and not any general topological space. Baby Rudin chapters 2-4 cover this pretty well.


Wait, are you sure? What about topologist's sine curve, Hausdorff, homeomorphisms, etc?

blahquaker
Posts: 24
Joined: Thu Jan 11, 2018 10:36 am

Re: Topology coverage in the GRE

Postby blahquaker » Mon Sep 17, 2018 10:10 am

there is very little topology on the exam. compact, connected, continuous are the main things. there could be a topological space, Hausdorff, metric, etc, but the chances of it being more than one question are very slim. if you're learning it solely for the mGRE, reading all of Munkres is not a good use of your time.

BCLC
Posts: 36
Joined: Mon Oct 24, 2016 1:10 am

Re: Topology coverage in the GRE

Postby BCLC » Mon Sep 17, 2018 10:17 am

blahquaker wrote:there is very little topology on the exam. compact, connected, continuous are the main things. there could be a topological space, Hausdorff, metric, etc, but the chances of it being more than one question are very slim. if you're learning it solely for the mGRE, reading all of Munkres is not a good use of your time.


It's not solely for the mGRE. Thanks a lot blahquaker!




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