Please try to clarify how is defined.
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?