(a) If  is a family of topologies on X, show that  is a topology on X.Is  topology on X?(b...

(a) If  is a family of topologies on X, show that  is a topology on X.Is  topology on X?

(b) Let  be a family of topologies on X. Show that there is a unique smallest topology on X containing all the collections  and a unique largest topology contained in all

(c) If X={a, b, c}, let

Find the smallest topology containing , and the largest topology contained in .