unfortunately, not really. you have to get comfortable with the basic definition. it might seem crude, but it was made up so that certain things would work.

of course, T is a topology on {1,2,3} because it satisfies the three axioms.

(1) the empty set and the set itself are in T

(2) The union of any number of elements in T is also in T

(3) The intersection of any (finite) collection of sets in T is in T.