5
$\begingroup$

I have started reading point-set topology from Topology-J.R.Munkres. I have read the chapter Countability and Separation Axioms and started doing the exercises on Article 30. I feel that I have understood the chapter but the problem is I have failed to work out any of the exercises on the chapter.

I started with the problem Prove that in a first countable $T_1$ space every singleton is a G$_\delta $ set which I have failed and I am also unsuccessful on the subsequent exercises.

Is it wrong to start with Munkres or the problem is somewhere else?

I am feeling very depressed as I can't proceed anymore.

Should I look for some other book? If so then please suggest some. Any advice will be helpful.

$\endgroup$
8
  • 4
    $\begingroup$ What is your background prior to reading the book? Have you had any introductory courses to real analysis? Although it is not necessary, that may help you get a better intuitive grasp of the abstract concepts. $\endgroup$
    – Future
    Dec 27, 2015 at 2:49
  • $\begingroup$ Have a look at this one for example: Seymour Lipschutz Schaums Outline of General Topology $\endgroup$
    – Mikasa
    Dec 27, 2015 at 2:52
  • 3
    $\begingroup$ One thing that has always helped me in topology: come up with a concrete example and try to prove the statement for your example. Then try to abstract to a more-general setting. In this case, give an example of a $T_1$ space. Prove in that example that a singleton is a $G_\delta$ set. What properties did you use that were inherent to the topological space? If none, you have your proof written. If you used some property, how can you avoid needing it? $\endgroup$
    – Clayton
    Dec 27, 2015 at 2:57
  • $\begingroup$ @T.S.L;I have read real analysis from Bartle Sherbert before $\endgroup$
    – Learnmore
    Dec 27, 2015 at 4:01
  • $\begingroup$ @Clayton;$\Bbb R$ is such an example then any $a\in \Bbb R$ is of the form $\{a\}=(a-\frac{1}{n},a+\frac{1}{n})$;How can I use this info? $\endgroup$
    – Learnmore
    Dec 27, 2015 at 4:07

1 Answer 1

Reset to default
0
$\begingroup$

I am currently working through Pugh's "Real Mathematical Analysis" right now, and the second chapter of the textbook is an introduction to topology. From what I can see, he bases a lot of the exercises in the end of the chapter off of relevant concepts in Munkres (he even makes specific references to Munkres throughout the text and exercises) and possibly other textbooks. It couldn't hurt to have that book to use to gain an intuition for the concepts you are struggling with, so that you can better attack Munkres.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged .