# Continuity of a metric space

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Prove: The function f from the metric space X into the metric space Y is continuous if and only if is closed in X whenever F is closed in Y.

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This solution is comprised of a detailed explanation to prove the function f from the metric space X into the metric space Y is continuous if and only if is closed in X whenever F is closed in Y.

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Prove: The function f from the metric space X into the metric space Y is continuous if and only if is closed in X whenever F is closed in Y.

Proof:

Let d and be metric in X and Y ...

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