Main Question or Discussion Point
Is calculus enough?
great news! Can you also suggest a textbook ? I've heard many people say topology by Munkres is the best one.There is no formal prerequisite except that if you haven't studied the topology of R and R^n and metric spaces first (as seen in elementary analysis courses), then the basic definitions of topology are going to be hard. In the sens that they will seem ferociously abstract and unmotivated.
The first chapter in the Topology by Munkres, covers pretty much everything you need to know on set theory and that will be essential in topology.I don't think regular, undergraduate Calculus is enough to learn topology. You really need either:
1. A proofs class or
2. A logic class and knowledge of sets