actually i just saw that to show the union part is pretty trivial. but i cannot seem to figure out the intersection part.
X is a set and T be the family of subsets U of X such that X\U is finite, together with the empty set. show that T, the cofinite topology of X, is a topology. i think that it is obvious that condition 1 holds, but i am finding it difficult to show condition 2 and 3 (any union of sets in T belongs to T and that any intersection of sets in T belong to T). thanks in advance for help!