# Prerequisites for learning general topology

I want to learn general topology in order to apply it in electromagnetism.
I am an undergraduate student and I have a background in linear algebra (not at an advanced level), linear differential equations, multivariable calculus, and probability theory.
What are the prerequisites for learning general topology?

Also, every textbook that I find on general topology states that its level is for graduate studies.
So, do you have any textbooks that are for undergraduate-level topology?
Thank you.

• There's Armstrong's "Basic Topology" which is the "Undergraduate Texts in Mathematics" series. But I think the book is rather difficult for an undergraduate. The hard part is not really the pre-requisite but the ability to read and write good clean proofs. How are you at proofs? If your proof skills need to be refined first, I suggest reading as elementary a book as you can find on "abstract algebra" because I think that's a subject that uses proofs but starts in a pretty basic way, basically square one. – Gregory Grant May 19 '15 at 10:23
• You have to be comfortable with the use of set theory. Would be great (but not necessary) if you know some $\epsilon -\delta$ argument. – user99914 May 19 '15 at 10:24
• There is a free book "Topology Without Tears" u.math.biu.ac.il/~megereli/topbook.pdf I would suggest reading Chapter 5 before Chapter 4. – Joe Johnson 126 May 19 '15 at 10:55
• @GregoryGrant i am pretty good at proofs.Although i will not be dealing with them at this level because all i want topology is for electromagnetism,which means i want to apply topology,so no mathematical proofs are required.I will surely check them out.I did proofs when studying the other subjects because i used those mathematics widely.But for this,i just want it for one subject,so no need to go THAT deep.To be more specific,i want to go as deep as learn linking numbers and the concept of helicity.Does your text include them(only linking numbers would be great) – TheQuantumMan May 19 '15 at 10:58
• @JoeJohnson126 does it have linking numbers? – TheQuantumMan May 19 '15 at 11:00

I think Electromagnetic Theory and Computation: A Topological Approach by Gross and Kotiuga might be just what you're looking for. However, it does assume that you know some general and algebraic topology to start with.

I would recommend that you read John Lee's Topological Manifolds first. The text covers what you would expect in a typical topology book, but focusing primarily on manifolds, which are the physicist's preferred sort of spaces. However, it can be a bit difficult for beginners, since it assumes mathematical maturity, so you may want to keep a more elementary reference like Munkres handy for when you get stuck.

Alternatively, you could read a more physicist-oriented introduction to topology like Nakahara's Geometry, Topology, and Physics. I have not personally read it, but it seems like it should be accessible for you. There is also Gauge Fields, Knots, and Gravity by Baez and Munian, which is a very well-written book that provides good intuition, but is more of a survey than a textbook for learning the details.

• Nakahara is a graduate's book,so it is difficult for me to read.Baez's book is good,so i will keep it beside me along Munkre's book and i will approach the subject the way that you suggested!Thanks a lot! – TheQuantumMan May 19 '15 at 11:42
• Are the rest of your suggested books on undergraduate level? – TheQuantumMan May 19 '15 at 11:57
• Lee's Topological Manifolds is also a graduate text, but it's probably the most appropriate for your goals in terms of its content. I think if you read it alongside Munkres (which is an undergrad text) it should be accessible. – ಠ_ಠ May 19 '15 at 12:15
• ok,thanks a lot! – TheQuantumMan May 19 '15 at 12:23
• Erica Flapan's book When Topology Meets Chemistry: A Topological Look at Molecular Chirality might be useful, perhaps as alternate reading for a gentler introduction to some of the topics. – Dave L. Renfro May 19 '15 at 16:20

All you need is some set theory and you're good to go.

Read Topology: A First Course by Munkres first, this develops all the set theory that you need to know to tackle General Topology.

Do not read Introduction to Manifolds by Lee as a first book, read that as a second book or as a companion to Munkres, the reason I say this as that it would be really difficult as a first exposure, but as a second exposure to General Topology it will be a delight to read and supplement your knowledge.