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Suppose d and d 0 are both metrics on X and that the metric spaces (X,...

Suppose d and d 0 are both metrics on X and that the metric spaces (X, d) and (X, d0 ) have the same open sets. Show, the sequence (an) from X converges in (X, d) if and only if it converges in (X, d0 ) and then to the same limit.

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