How many topologies can be made with

a set that has 2 points, and a set that has 3 points, and a set that has 4 points??

My guess for the 2 points are if A = {a,b}

topology of A can be {emptyset, {a,b}} or {emptyset, {a}, {b}}.

but can the set {emptyset, {a}} be a topology of A? thank you