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Real Analysis : In this space, is every closed and bounded set compact?

Let (X,d) be the metric space consisting of m-tuples of real numbers with metric
d(x,y)=max{|a_k-b_k|:k=1...m}
where x={a_1, a_2,...,a_m} and y={b_1, b_2,...,b_m}.
In this space is every closed and bounded set compact?

keywords: Heine-Borel, Borel

Solution Preview

The answer is yes.
This can be induced directly by Heine-Borel ...

Solution Summary

Compactness in a metric space is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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