The usual proof of this theorem seems to assume that the topology of the metric space is the one generated by the metric. But if I use another topology, for example the trivial, the space need not be Hausdorff but the metric stays the same. Am I missing something or is the statement of the theorem just sloppy?(adsbygoogle = window.adsbygoogle || []).push({});

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# Every metric space is Hausdorff

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