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

Let l∞ be the space of bounded sequences of real numbers, endowed with the norm

∥x∥∞ = supn∈N |xn | , where x = (xn )n∈N .

Prove that the closed unit ball of l∞ , B(0, 1) = {x ∈ l∞ ; ∥x∥∞ ≤ 1} , is not compact.

2. Relevant equations

3. The attempt at a solution

I'm thinking about using the notion of sequential compactness, since every sequence Xn has an upper limit here, but I'm not sure if that would help much. Could anyone please give me a hint? Any input is appreciated!

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# Homework Help: Compactness of closed unit ball

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