1 (a)

Let be a collection of subset of the set X, satisfying:

i. and X contained in ,

ii. finite unions of elements in are in , and

iii. arbitrary unions of elements in are in [

Show that the collection

is a topology on X.

(b)

Give an example of such a topology when X = . What are the open sets in this topology?What are the closed sets? What is the basis for the topology?