1. Prove that, in a topological space X, if U is open and C is closed, then U - C is open and C - U is closed.
2. Which sets are closed sets in the finite complement topology on a topological space X?
3. Let X be a topological space.
(a) Prove that Φ and X are closed sets.
(b) Prove that the intersection of any collection of closed sets in X is a closed set.
(c) Prove that the union of finitely many closed sets in X is a closed set.
4. Show that R in the lower limit topology is Hausdorff.
5. Show that R in the finite complement topology is not Hausdorff.
6. Which sets are closed sets in the particular point topology PPX p on a set X?