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.
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.