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.
 A: You should know basic operations in set theory.
For example, do you think that:
$f(A\cup B)=f(A)\cup f(B)\: ? \:   f(A\cap B)=f(A)\cap f(B)\: ? \:f(f^{-1}(S))=S\:? \: f^{-1}(f(T))=T \:?$  
...and can you state a precise context in which these questions make sense?
A: Set theory (naive set theory is fine for the most part, axiomatic set theory can sometimes be relevant) and a good grounding in reading and writing mathematical proofs are the two essentials for point-set topology.
Anything else you know won't be strictly necessary, but it will put definitions and examples in the proper context. Some knowledge of calculus or real analysis gives you a feel for the abstract definitions of convergence and continuity. If you know some group theory you will be able to talk about topological groups and orbit spaces, which gives you more examples of topological spaces to think about. You will also be able to get into algebraic topology later on.
Topology is a subject where understanding basically rests on the number of examples you have handy, and also a very widely encompassing subject. So with more background in other subjects you will have an easier time with obtaining a conceptual understanding.
