Can we find a norm that makes the space of all real sequences a Banach space?
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I think not, since this space would contain the space $\ell^{p}$ for $p<1$ which I believe is known to be only metrisable. – Calvin Khor Sep 03 '16 at 04:04
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4See this. – David Mitra Sep 03 '16 at 05:45