Quote by St41n
Which means that all possible open sets (or open balls) in a metric space (X,d) will form the topology τ of the induced topological space?
Is that correct?

Saying: "or open balls" is incorrect, the rest is correct. We say that a topology T on a space X is induced by a metric d on X iff the open balls generated by d forms a BASIS for the topology T (i.e. a set U is open iff it's a union of open balls).