Let http://www.mathhelpforum.com/math-he...c84d99af-1.gif be a collection of subset of the set X, satisfying:

i. http://www.mathhelpforum.com/math-he...2cc525ec-1.gif and X contained in http://www.mathhelpforum.com/math-he...c84d99af-1.gif,

ii. finite unions of elements in http://www.mathhelpforum.com/math-he...c84d99af-1.gif are in http://www.mathhelpforum.com/math-he...c84d99af-1.gif, and

iii. arbitrary unions of elements in http://www.mathhelpforum.com/math-he...c84d99af-1.gif are in http://www.mathhelpforum.com/math-he...c84d99af-1.gif

We know that http://www.mathhelpforum.com/math-he...a7af72c3-1.gif is a topology on X

Give an example of a topology when X = http://www.mathhelpforum.com/math-he...a3150bfd-1.gif. What are the open sets in this topology?What are the closed sets? What is the basis for the topology?