The question on the definition of a topological space has been appeared many times on this site, but I was unable to get answer to a natural question which not only I but a new learner of this subject can raise.
In the definition of a topology $\tau$ on a set $X$, there are condition on the family $\tau$ of subsets of $X$:
the family $\tau$ should contain empty set and $X$;
the family $\tau$ should be closed under arbitrary union and finite intersection.
The natural question is, why these conditions were chosen for the definition of a topological space?
It is fine that the open balls/sets in metric spaces satisfy above conditions; but it is not easy to convince to a new learner that exactly these properties motivated the definition of topology/topological space.
In different related question or books on topology, one can find similar type of motivation for the definition of topology, but I was not satisfied with it.
Can one explain in better way how these conditions were chosen for the definition of topology? (Means, why not less than these, no other than these, and not more than these?)