Solution
= Solution
\b[Not compact.] For coordinate unit vectors $e_j$ with $j\geq2$, the images are $e_{j-1}$. Distinct such images have $\ell^1$ distance two, so no image subsequence converges.
= Solution
\b[Not compact.] For coordinate unit vectors $e_j$ with $j\geq2$, the images are $e_{j-1}$. Distinct such images have $\ell^1$ distance two, so no image subsequence converges.