Consider the set X={a,b}, and the collection £ given by £={ Ø, {a},{b},X }. show that £ is a topology on X.
I know that from the definition of topological space i must consider to show the following three axioms
- To show that both the empty set and X belong to £
2.To show that the intersection of any finite sub-collection of sets in £ belong to £
3.To show that the union of any sub-collection of sets in £ belong to £
For the first axiom, it is true that both the empty set and X belong to £, and i have no problem with this.
but my problem lies on second and third axioms,i need to be clear, how can the sub-collections in axioms 1 and 2 be formed?
thanks!