Proving Inverse Function Continuity: A Topological Challenge

[stgermaine]

Homework Statement

Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous.

Homework Equations

I have no idea.

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.

 

[micromass]

Maybe start by giving the definition of a continuous function? What is it that you need to prove?

Also start by defining basis.