Let X be a topological space. (1) Show that the union of finite number of compact subsets of X is compact. (2) Let (Cafael be a family of subsets of X, where each Co is a closed and compact subset of X. Show that aer Ca is a closed and compact subset of X. Hint for Problem 3. (1) Show it directly. (2) First, show that it is closed. Then use Prop.V.5...