Thanks, I think I got it.
If T=\capTa, then:
1. 0 (empty set) and X \inT, since 0, X \in all Ta
2. If U1, U2\in T, then U1, U2\in all Ta; their intersection must be in all Ta as well (as is the defn. of a topology), so U1\capU2\in\bigcapTa
3. you gave me.
For the next question...
Hey guys, I'm reading Munkres book (2nd edition) and am caught on a problem out of Ch. 2. The problem states:
If {Ta} is a family of topologies on X, show that (intersection)Ta is a topology on X. Is UTa a topology on X?
Sorry for crappy notation; I don't know my way around the symbols...