1. The problem statement, all variables and given/known data Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous. 2. Relevant equations I have no idea. 3. The attempt at a solution I seriously have no idea. This is for my analysis course, and I'm not sure why the prof is going over topology. I have some PDF's so I have some idea about open sets and continuous functions but not enough to solve this proof.