Metric Space and Countable Dense Subset : Prove that if a metric space M is totally bounded, then there is a countable dense subset of M.
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2. Prove that if a metric space M is totally bounded, then there is a countable dense subset of M.
Note: we are using the "Methods of Real Analysis by Richard R Goldberg
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A Metric Space and Countable Dense Subset are investigated. The solution is detailed and well presented.
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Proof:
Since is a metric space and is totally bounded, according to the definition of "totally bounded", for any , we ...
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