need help with these

(a) Let f : X > Y be a function, and suppose X and Y are topological spaces with topologies 'IX and (Ty, respectively. Which of the following is equivalent to the condition that f be continuous? (Check all that apply.) 1. For any open U C Y, we have that f _1(U) is an open subset of X. 2. For any V C Y, we know that V E (Ty => f'1(V) E 'J'X. 3. Whenever B C Y is open, we know that the preimage of B is open. 4. Whenever B C Y is closed, we know that the preimage of B is closed. 5. Whenever U C X is open, we know that f (U) C Y is open. (b) Let X be a topological space. Which of the following implies that a subset B C X is closed? (Check all that apply.) 1. B = X. 2. B = 0. 3. B is an intersection of finitely many closed sets. 4. B is an intersection of closed sets. 5. B is a union of finitely many closed sets. 6. B is a union of closed sets. 7. B is a union of finitely many open sets. 8. B has infinitely elements in it. 9. B has finitely many elements in it. 10. The complement of B is open.(c) Let X = R" with the standard topology. Which of the following implies that a subset B C X is closed? (Check all that apply.) 1. B = X. 2. B = 0. 3. B is an intersection of finitely many closed sets. 4. B is an intersection of closed sets. 5. B is a union of finitely many closed sets. 6. B is a union of closed sets. 7. B is a union of finitely many open sets.8. B has infinitely elements in it. 9. B has finitely many elements in it. 10. The complement of B is open