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Is calculus enough?
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.
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