(Kuratowski) Consider the collection of all subsets A of the topological space X. The oper...

(Kuratowski) Consider the collection of all subsets A of the topological space X. The operations of closure A → Ā and complementation A → X − A are func­tions from this collection lo itself.

(a) Show that starting with a given set A, one can form no more than 14 distinct sets by applying these two operations successively.

(b) Find a subset A of  (in its usual topology) for which the maximum of 14 is obtained.