Question: I need to prove this: Suppose f:S->T is function mapping from a metric space to another. Prove that f is continuos on S if, and

I need to prove this:

Suppose f:S->T is function mapping from a metric space to another. Prove that f is continuos on S if, and only if, f^-1(B) is contained in (f^-1(B)) for every subset B of T. Please note: The symbol means the interior of a set.

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