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Prove the given theorem

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Reference no: EM131582627

Question: Prove Theorem.

Theorem: Equivalent metrics preserve open sets. Let X be a nonempty set, and d1 and d2 two metrics defined on it. Then a necessary and sufficient condition for d1 and d2 to be topologically equivalent is the following: A subset A of X is d1-open if and only if it is d2-open.

Reference no: EM131582627

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