# James R. Munkres' TOPOLOGY, 2nd edition: How to check my work?

I'm trying to learn, or revise, some topology from James R. Munkres' TOPOLOGY, 2nd edition. I'm working alone; that is, I'm self-learning. It is quite fun. But the problem is how do I check if I've managed to arrive at a correct solution to an exercise problem? Can I get hold of a solution manual? Or, can I find someone over the Internet with whom I can discuss my solutions? Of course, putting up every other problem at Mathematics Stack Exchange, it seems to me, is not so practical!

What would be the best possible for me?

• Many of Munkres problems have solutions posted some where online. Just googling the problem will usually work. Additionally, there was a guy who went to Drexel and transferred to UM with the first name of Alex. He has a blog that has full solutions to Munkres as well. I found it: drexel28.wordpress.com/about Nov 5, 2014 at 15:09
• @dustin, how complete are these solutions? And, how correct are these? Nov 5, 2014 at 15:17
• Solution manuals are not usually too helpful for checking your work in a proof-based subject. Often you'll just find you have a different proof from the solution you're reading; it doesn't tell you whether yours is correct or not. Nov 5, 2014 at 15:22
• How to determine if your answer is correct? Give a proof that it is! (In a textbook like Munkres, every exercise should be a proof. A question like "Is this set countable?" should be read as "Give a proof that the set is countable, or a proof that it is not.") Nov 5, 2014 at 16:27
• @NateEldredge, what if I inadvertently reach an erroneous conclusion? How would I know that I've not gone wrong? Nov 6, 2014 at 19:13

If you already got a solution/proof, I would just go check it another time, and another time. Imagine you are explaining your proof to someone really skeptical. And try to convince this most skeptical part of yourself.

I don't think you need someone else, except if you are really stuck on some exercise, and don't know how to proceed. In that case, you can use this site.

• due to my eyesight problem, I'm not so comfortable writing up the solutions; so I do most of them in my head, jotting the lengthier calculations but only occasionally. So each time I return to an exercise, I have to start all over again. Nov 5, 2014 at 15:56

Here is another solution manual: https://math.solverer.com/library/james_munkres/topology_classic_version

You can find solutions of most of them in the following link: http://dbfin.com/topology/munkres/

• the site is died Feb 3, 2021 at 6:17
• the link is no longer active Sep 10, 2022 at 20:09

If anyone is interested, I wrote down solutions to exercises in Chapters 2 and 3.

You can find them here: https://positron0802.wordpress.com/topology-munkres/

I learned general topology exactly in this way, and basically I'm a topologist now! I remember that I never needed to check if the solutions were correct because most of those exercises were straightforward. My advice is: try to correct your solutions by yourself. Just write down extensive solutions of your problems, and double check each step asking to yourself: "which property/theorem/lemma am I using here?".