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We are working with the following question for an exercise:

We got the definition: A subset $K$ in a metric space $(M,d)$ is called precompact if for every $\epsilon > 0$ there exist finitely many points $x_1, \dots , x_p \in K$ such that $K \subset B_\epsilon(x_1) \cup \dots \cup B_\epsilon(x_p)$.

We then have to show that a subset $K \subset\Bbb R^n$ in the space $\Bbb R^n$ (with Euclidean metric) is precompact if and only if it is bounded.

David C. Ullrich
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SoNoob
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  • To some extend, but im not totally sure that i understand the proof the way where you have to show that it is precompact if it is bounded, could you help clarify that part? – SoNoob Jan 14 '20 at 11:51
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    Are asking me to explain the whole proof while you give me no clue about which part you failed to understand? That is not a reasonable request. – José Carlos Santos Jan 14 '20 at 11:55

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