(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume some metric space (K,d) obeys Lindelof, take (X,d) a metric subspace of (K,d) and show it too must obey Lindelof.

3. The attempt at a solution

I'm assuming since I know that (K,d) obeys Lindelof then there is some open cover that has a countable subcover say {J_{i}| i is a positive rational number}. Since this covers all of the metric space, then it surely covers the metric subspace. So I'm thinking all I need to really prove is that the elements of this set of open countable covers is open under metric subspace (X,d)? Or do I need to show that I can select a countable number of {J_{i}} to cover (X,d)? If so, any suggestions on how to do so?

This is the last assignment question, and it's due this Wednesday November 2nd, any help would be appreciated!

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# Metric Space and Lindelof Theorem

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