Question

Let X={1,2,3,4} and A={{1,2},{2,4},{3}}. Determine the topology on X generated by A as a subbase and hence determine the base for this topology.​

Answer 1

Answer:

Definition: A subbasis S for a topology on X is a collection of subsets of X whose union is X.

So let S be equal to the collection of {a,b}, {c,d} and {d,e}.

Clearly union of these three elements is X.

So should be S - as defined - be taken as subbasis?