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Maximum and minimum mapping

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Prove: A continuous mapping T of a compact subset M of a metric space X into assumes a maximum and a minimum at some points of M.

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This is a proof that a continuous mapping with given conditions assumes a maximum and minimum.

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Prove: A continuous mapping T of a compact subset M of a metric space X into assumes a maximum and a minimum at some points of M.

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First, we know, is a ...

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