What path to get to topology? I am in calc 1 right now and was wondering what kind of journey is ahead of me before topology. I really want to study high level math like this but am not sure if I want to major in math. I am a pre med student so I need my 4.0 to continue all throughout college in order to get into med school so majoring in math might not be a good idea.
 A: As pointed out in a comment, the only strict requirements for topology are basic set theory knowledge, and mathematical "maturity", i.e. ability to understand and write proofs. However, in topology you will encounter seemingly weird definitions, e.g. a function is continuous if the pre-image of every open set is open, and if you haven't taken real analysis then it will be hard to see why this is the appropriate definition. Same for some other topology definitions too, e.g. why an arbitrary union of open sets is defined to be open but only finite intersections of open sets are defined to be open. So I'd say take a course or go through a book on real analysis first, and if you haven't had much exposure to understanding/writing proofs then first take an introduction to higher mathematics course if one is offered. (Where you basically just learn how to write proofs.) My university offered such a course and I took it before all my higher mathematics classes and I'm really glad I did. Proof-writing often requires some initiation to get acquainted.
