INverse of a function between topological spaces and continuity

[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

The Attempt at a Solution

I really don't know how to do this. Wikipedia entry for 'base sets' redirects to Pokemon cards.

 

[Bacle2]

Have you tried playing with the Pokemon cards?

Just kidding; the standard def. of continuity , AFAIK, is that f:X-->Y is continuous

iff.(def.) the inverse image of an open subset of Y is open in X. Do you know how

basic sets relate to open sets?