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The metric space M is separable if it contains a countable dense subset. [Note the confusion of...

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Advance Math

The metric space M is separable if it contains a countable densesubset. [Note
the confusion of language: “Separable” has nothing to do with“separation.”]
(a) Prove that R^m is separable.
(b) Prove that every compact metric space is separable.

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