# Math Help - question about general topological spaces

1. ## question about general topological spaces

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!

2. actually i just saw that to show the union part is pretty trivial. but i cannot seem to figure out the intersection part.

3. BTW: The third condition says finite intersection.
If each of O & Q is cofinite then $\left( {O \cap Q} \right)^c = O^c \cup Q^c$. The union of two finite sets is a finite set.