# What are the suggested prerequisites for topology?

I am interested in topology but I don't know if I can learn it without learning something else first.

I've done: Algebra 1 and 2 Euclidean Geometry Calculus

Is that enough if not please tell me what else I need to learn.

• Ask your teacher, no general answer can be given. – Michael Greinecker Dec 11 '14 at 19:10
• For point-set topology, there are almost no pre-reqs, other than the ability to reason from definitions. Algebraic topology requires abstract algebra (it's not clear what you mean by Algebra, but it sounds like you are using the high school term, which is different from abstract algebra.) – Thomas Andrews Dec 11 '14 at 19:11
• The only thing I would suggest is to have had a course which emphasizes formal proof. This is typically what is called "Advanced Calculus" or "Analysis", and is usually a upper-level undergraduate course. Don't let the word "calculus" in the title mislead you -- it isn't the calculus you typically see in high school or undergraduate calculus courses; it's focus is "grown-up" rigorous mathematical techniques. If you don't know them, you will have a hard time in a topology course. That said, it of course depends on the level of difficulty of the particular course you are considering. – MPW Dec 11 '14 at 19:18
• I'd say you should have some understanding of how mathematical proofs are written and some acquaintence with naive set theory. – Michael Hardy Dec 11 '14 at 19:24

$f(A\cup B)=f(A)\cup f(B)\: ? \: f(A\cap B)=f(A)\cap f(B)\: ? \:f(f^{-1}(S))=S\:? \: f^{-1}(f(T))=T \:?$