well, start with the basics, what is a topology? it is a pair of a set and a set of "open" subsets of , which we denote here, , such that we have the following axioms holding:

(1) arbitrary unions of open sets are open

(2) the intersection of any two open sets is open

(3) and are open

so really, counting the elements in a topology amounts to counting subsets of a set, , and the numbers of subsets we can form from the subset of the set . of course, the subset has to contain at least and .

now do you think you can answer your problem?