I What chapters of Munkres Topology are essential?

[cpsinkule]

I would like to know which chapters in Munkres Topology textbook are essential for a physicist. My background in topology is limited to the topology in baby Rudin, Kreyzig's functional, and handwavy topology in intro GR books. I feel like the entire book isn't necessary, but I could be mistaken.

 

[Demystifier]

A physicist, even a mathematical physicist, can live without ever reading Munkres or anything equivalent. Books entitled "Topology for physicists" or something alike should be sufficient, and such books do not pay much attention to things studied in Munkres-like books. But of course, if you want to know more topology than a physicist really needs to know, you are welcome to read Munkres or anything else which you find interesting.

 

[cpsinkule]

A physicist, even a mathematical physicist, can live without ever reading Munkres or anything equivalent. Books entitled "Topology for physicists" or something alike should be sufficient, and such books do not pay much attention to things studied in Munkres-like books. But of course, if you want to know more topology than a physicist really needs to know, you are welcome to read Munkres or anything else which you find interesting.

I would like to learn differential geometry the mathematicians way, not the physicists way. I usually just gloss over passages about Hausdorff spaces, second countable, paracompact and things of that nature and I would like to stop doing that.

 

[dkotschessaa]

Note that I don't have a physics background, but I'm buried in Munkres right now.

Based on what you've said here I'd think you'd want 2-4 of Munkres and then maybe 6 (since you mentioned paracompact). 6 is not dependent on 5, but 5 is short.

Chapter 1 is a review of set theory and logic and might still be helpful if not for the review itself then to know what conventions he uses later.

It doesn't sound like you need algebraic topology, but the essentials are in chapter 9.

Check his preface for some of his own recommendations.

-Dave K

 

[Demystifier]

I would like to learn differential geometry the mathematicians way, not the physicists way.

That's fine, but I don't think that learning math the non-physicist way can be essential for physics. Maybe useful, complementary, or deepening, but not essential.

 

[lavinia]

I inadvertently replied to your question on the wrong thread although it seems to be OK there so I left it. Here is the link.

https://www.physicsforums.com/threa...he-practical-application.897969/#post-5649149