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P: 424
 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).