Let X be a set. Consider the following family T of subsets of X: T = {0}U {OCX | XO is a countable set}. (The family T is called the countable complement topology.) (a) Show that T is a topology. (b) Show that if AC X is a countable subset, then the derived set A' is empty. (c) Show that if AC X is an uncountable subset, then A' = X.